What is the volume of the cone with diameter 26 m and height 28 m? Round to the nearest cubic meter.

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Lesson 1: Volume of Cylinders

• • Volume of Cylinders – Page No. 402
  • Book of Cylinders – Page No. 403
  • Book of Cylinders – Folio No. 404

Lesson 2: Volume of Cones

• • Volume of Cones – Page No. 408
  • Book of Cones – Folio No. 409
  • Volume of Cones – Page No. 410

Lesson 3: Volume of Spheres

• • Volume of Spheres – Folio No. 414
  • Volume of Spheres – Page No. 415
  • Book of Spheres – Page No. 416

Model Quiz :

• • Model Quiz – Page No. 417

Review :

• • Mixed Review – Folio No. 418

Guided Practice – Volume of Cylinders – Page No. 402

Question 1.
Vocabulary Describe the bases of a cylinder.
Type below:
____________

Answer:
The ends of a cylinder are the bases of the cylinder of the two apartment surfaces.

Question 2.
Figure one shows a view from to a higher place of inch cubes on the bottom of a cylinder. Figure ii shows the highest stack of cubes that will fit inside the cylinder. Estimate the volume of the cylinder. Explain your reasoning.

________ in³

Answer:

427in³

Explanation:
Number of inch cubes that fit in the base of the cylinder = 61
Number of inch cubes that fit in the length of the cylinder = 7
Volume of cylinder = basearea x tiptop
V= 61 x seven
Five = 427 cubic units.
Volume of each cube = one in³
Volume of cylinder = 427in³

Question 3.
Find the volume of the cylinder to the nearest tenth. Use iii.xiv for π.

The volume of the cylinder is approximately _____ m³.
________ yardⁱⁱⁱ

Respond:
The volume of the cylinder is approximately 1695.6 mⁱⁱⁱ.
1695.6m³

Explanation:
V = πr²h
V = π . 6² . 15
V = 3.xiv × 36 × 15
V = 1695.6m³

Question 4.
A Japanese odaiko is a very large drum that is fabricated by hollowing out a department of a tree trunk. A museum in Takayama Metropolis has three odaikos of similar size carved from a single tree torso. The largest measures about 2.7 meters in both bore and length, and weighs about iv.5 metric tons. Using the volume formula for a cylinder, approximate the volume of the drum to the nearest tenth.
The radius of the drum is virtually _____ m.
The volume of the drum is about _____ m³.
The radius of the drum is virtually ___________ m
The volume of the drum is about ___________ thousand³

Answer:
The radius of the pulsate is about i.35 m.
The volume of the drum is about 15.five thousand³.

Caption:
Diameter of base of operations of drum = two.seven yard
The radius of the base of the drum = two.7/ii
R = 1.35 yard
The volume of cylinder = πr²h
Height (h) = 2.vii thousand
Radius (R) = ane.35 1000
Book = 3.fourteen × (1.35) × 2.7
V = xv.4511 one thousand³
V = 15.5 m³

ESSENTIAL QUESTION CHECK-IN

Question 5.
How practice you notice the volume of a cylinder? Draw which measurements of a cylinder you need to know.
Type beneath:
____________

Answer:
The volume of the cylinder is = πr²h

Explanation:
We need to find the radius of the base, r, and the height of the cylinder, h.
The book of the cylinder is = πr²h

13.1 Independent Do – Book of Cylinders – Page No. 403

Observe the book of each effigy. Round your answers to the nearest tenth if necessary. Utilize 3.14 for π.

Question half dozen.

_________ cm^three

Answer:
569.ix cm³

Caption:
Radius of base = xi cm
Height of cylinder = 1.5 cm
The volume of cylinder = πr²h
V = 3.xiv × (11)² × 1.5
5 = 569.91
V = 569.9 cm³

Question 7.

_________ in³

Reply:
1205.viii in³

Explanation:
Radius of base of operations = 4 in
Height of cylinder = 24 in
The volume of cylinder = πr²h
V = 3.14 × (4)² × 24
V = 1205.76
V = 1205.8 in³

Question 8.

_________ thousand³

Answer:
1256 m³

Caption:
Radius of base = 5 m
Acme of cylinder = xvi chiliad
The volume of cylinder = πr²h
5 = three.xiv × (5)² × sixteen
5 = 1256
5 = 1256 m³

Question 9.

_________ in³

Answer:
942 in³

Explanation:
Diameter of base of operations = 10 in
Radius of base = 5 in
Height of cylinder = 12 in
The book of cylinder = πr²h
5 = three.xiv × (5)² × 12
V = 942 in³

Question 10.
A cylinder has a radius of 4 centimeters and a elevation of 40 centimeters.
_________ cmⁱⁱⁱ

Reply:
2009.half-dozen cm³

Explanation:
Radius of base = 4 cm
Height of cylinder = 40 cm
The volume of cylinder = πr²h
V = 3.14 × (4)² × 40
V = 2009.half-dozen cm³

Question xi.
A cylinder has a radius of viii meters and a height of iv meters.
_________ thousand^three

Answer:
803.8 k³

Explanation:
The radius of base = 8 1000
Superlative of cylinder = four m
The volume of cylinder = πr²h
V = iii.xiv × (8)² × 4
5 = 803.84 m³
V = 803.eight thousand³

Round your answer to the nearest tenth, if necessary. Use 3.14 for π.

Question 12.
The cylindrical Giant Body of water Tank at the New England Aquarium in Boston is 24 anxiety deep and has a radius of 18.8 anxiety. Find the volume of the tank.
_________ ft³

Answer:
26635.ii ft³

Explanation:
Base radius of the tank = 18.viii ft
Depth of the tank in the sea = 24 ft
The volume of cylinder = πr²h
V = three.14 × (18.8)² × 24
V = 3.14 × 354.44 × 24
V = 26635.2384 ft³
V = 26635.2 ft³

Question 13.
A standard-size bass drum has a diameter of 22 inches and is 18 inches deep. Find the volume of this drum.
_________ in³

Answer:
6838.9 in³

Explanation:
Base diameter of pulsate = 22 in
Base radius of the drum = 22/two = 11 in
Depth of the bass drum = eighteen in
Volume of the bass drum = πr²h
5 = 3.14 × (11)² × 18
Five = 3.14 × 121 × xviii
V = 6838.92 in³
V = 6838.9 in³

Question fourteen.
Grain is stored in cylindrical structures called silos. Notice the volume of a silo with a diameter of 11.ane feet and a summit of xx feet.
_________ ft³

Answer:
1934.four ft³

Explanation:
Base of operations diameter of silo = 11.1 ft
Base radius of the silo = 11.one/2 = v.55 ft
Depth of the silo = 20 ft
Volume of the silo = πr²h
V = 3.14 × (5.55)² × 18
Five = 3.14 × 30.8025 × eighteen
V = 1934.397 ft³
V = 1934.4 ft³

Question 15.
The Frank Erwin Middle, or "The Drum," at the University of Texas in Austin can exist approximated by a cylinder that is 120 meters in diameter and xxx meters in pinnacle. Notice its book.
_________ m³

Answer:
339120 m³

Explanation:
Base bore of the drum = 120 m
Base of operations radius of the drum = 120/2 = 60 1000
Summit of the drum = 30 1000
Volume of the drum = πr²h
V = 3.14 × (60)² × 30
V = 3.xiv × 3600 × 30
V = 339120 one thousand³

Book of Cylinders – Folio No. 404

Question 16.
A barrel of crude oil contains almost 5.61 cubic anxiety of oil. How many barrels of oil are contained in ane mile (5280 feet) of a pipeline that has an inside diameter of 6 inches and is completely filled with oil? How much is "1 mile" of oil in this pipeline worth at a cost of $100 per barrel?
__________ barrels
$ __________

Answer:
184.7 barrels
$18470

Caption:
Volume of butt = 5.61 cubic feet
Length of the pipe = 1 mile = 5280 feet
Bore of the pipe = vi inches = 0.5 anxiety
Radius of the pipe = 6/ii inches = three inches = 0.25 anxiety
Volume of oil in the pipage = πr²h = three.14 × (0.25)² × 5280 = 1036.ii cubic feet
Number of barrels in the pipage = 1036.2/5.61 = 184.7 barrels
Cost of one barrel = $100
Cost of 184.7 barrels =184.seven × $100 = $18470

Question 17.
A pan for blistering French bread is shaped like half a cylinder. It is 12 inches long and 3.5 inches in diameter. What is the volume of uncooked dough that would fill this pan?

_________ in³

Answer:
57.697 in³

Caption:
The length of the pan = 12 in
The diameter of the pan = 3.5 in
Radius = 3.5/2 = 1.75 in
The volume of uncooked dough = Half the volume of the full cylinder of the above dimensions.
= (πr²h)/2 = (3.14 × (one.75)² × 12)/2 = 115.395/2 = 57.697 in³

FOCUS ON HIGHER ORDER THINKING

Question 18.
Explain the Error A student said the volume of a cylinder with a iii-inch diameter is two times the book of a cylinder with the aforementioned height and a 1.5-inch radius. What is the error?
Type below:
_______________

Answer:
The book of the cylinder of iii in is 4 times the volume of the new cylinder of radius 1.5 in

Explanation:
The volume of a cylinder is straight proportional to the square of the radius of the cylinder. The volume does not depend on the radius linearly.
Book = πr²h
V1 = π(3)²h
V2 = π(1.v)²h
V1/V2 = (π(3)²h)/(π(1.5)²h)
V1/V2 = 4
V1 = 4V2

Question 19.
Communicate Mathematical Ideas Explain how you tin can find the superlative of a cylinder if you know the diameter and the volume. Include an example with your caption.
Blazon beneath:
_______________

Respond:
Allow the diameter be D.
Radius r = D/two
Volume = πr²h
Volume = π(D/2)²h
V = π((D)²/4)h
h = 4V/π(D)²
To find the superlative of a cylinder with diameter D = two m
Allow the book be 10 m³
h = 4V/π(D)²
h = (four × 10)/(three.fourteen × 2²)
h = 3.xviii m³

Question 20.
Analyze Relationships Cylinder A has a radius of vi centimeters. Cylinder B has the same height and a radius half as long as cylinder A. What fraction of the volume of cylinder A is the volume of cylinder B? Explain.
Fraction: \(\frac{□}{□}\)

Respond:
\(\frac{VA}{4}\)

Explanation:
rA = 6 cm
rB = half of the radius of cylinder A = 3 cm
hA = hB
VA = πrA²h
VB = πrB²h
VA/VB = (πrA²h)/(πrB²h)
VA/VB = half-dozen²/3² = 36/nine = 4
Thus VB = VA/4

Guided Practise – Volume of Cones – Page No. 408

Question 1.
The surface area of the base of a cylinder is 45 square inches and its meridian is ten inches. A cone has the same area for its base and the same summit. What is the volume of the cone?

The volume of the cone is _____ in³.
_________ inⁱⁱⁱ

Reply:
150 in³

Explanation:
In the question, the area of the base of the cylinder, B = 45 in²
Elevation of the cylinder, h = 10 inch
Volume of the cylinder, V cylinder = B × h = 45 × 10 = 450 inch³
Book of the cone, 5 Cone = i/3 V cylinder
=1/3(450 inch) = 150 inch³
So, the volume of the cone is
Vcone = 150 in³

Question 2.
A cone and a cylinder have congruent tiptop and bases. The volume of the cone is xviii thou³.What is the volume of the cylinder? Explain.
_________ chiliad^three

Answer:
54 one thousand^three

Explanation:
The volume of the cone is 18 m³.
Vcone = 1/3 Vcylinder
Vcylinder = 3Vcone
Vcylinder = 3.18
Vcylinder = 54 grand^three

Find the volume of each cone. Round your reply to the nearest tenth if necessary. Use three.14 for π.

Question 3.

_________ ft^three

Answer:
65.94 ft³

Explanation:
the diameter of the cone is 6ft.
and so, the radius of the cone is 3ft.
the superlative of the cone is 7ft.
the book of the cone = 1/3 × πr²h = 1/3 × iii.fourteen × 3² × vii = 65.94 ft³

Question four.

_________ in³

Answer:
113982in³

Caption:
The radius is 33inch and the pinnacle is 100 inch
Volume of the cone = 1/3 × πr²h = i/3 × π(33)²100 = 113982in³

Question 5.
Gretchen made a paper cone to concur a gift for a friend. The paper cone was 15 inches high and had a radius of 3 inches. Discover the book of the paper cone to the nearest tenth. Use iii.14 for π.
_________ in³

Respond:
141.3in³

Explanation:
the radius of the cone is 3inch and the height of the cone is 15inch.
Volume of the cone = 1/iii × πr²h = 1/3 × π(three)² × fifteen = 141.3in³

Question half dozen.
A cone-shaped building is unremarkably used to store sand. What would be the book of a cone-shaped building with a diameter of 50 meters and a height of xx meters? Circular your respond to the nearest 10th. Utilise 3.xiv for π.
_________ m³

Answer:
13083.33 one thousand³

Explanation:
The diameter of the cone is l meters. So, the radius of the cone is 25 meters. The peak of the cone is 20 meters.
Book of the cone = i/3 × πr²h = ane/three × π(25)² × 20 = 13083.33 m³

ESSENTIAL QUESTION CHECK-IN

Question vii.
How do you notice the volume of a cone?
Type below:
____________

Reply:
Five cone = 1/three Five cylinder
V cone = 1/3 πr²h

xiii.2 Independent Do – Volume of Cones – Page No. 409

Find the book of each cone. Round your answers to the nearest tenth if necessary. Use iii.14 for π.

Question eight.

_________ mm³

Answer:
410.three mm³

Explanation:
Radius r = 7 mm
height = 8 mm
Volume of cone = 1/iii πr²h
Volume = 1/3(3.xiv)(seven)²(8)
Volume = 410.29 mm³
Volume = 410.3 mm³

Question 9.

_________ in³

Reply:
25.1 in³

Explanation:
Radius r = ii in
Height = 6 in
Volume of cone = 1/3 πr²h
Book = 1/3(3.14)(ii)²(6)
Volume = 25.12 in³
Volume = 25.one inⁱⁱⁱ

Question ten.
A cone has a diameter of 6 centimeters and a height of eleven.5 centimeters.
_________ cm³

Respond:
108.3 cm^three

Explanation:
Bore of base of operations = half dozen cm
Radius = six/2 cm = 3 cm
Height = 11.5 cm
Book of cone = 1/iii πr²h
Volume = 1/3(iii.14)(3)² (xi.5)
Volume = 108.33 cm^three
Book = 108.three cm³

Question eleven.
A cone has a radius of 3 meters and a height of 10 meters.
_________ m^three

Respond:
94.2 thousand³

Explanation:
Radius r = 3 m
Top = 10 grand
Volume of cone = 1/3 πr²h
Volume = 1/3(iii.14)(3)²(x)
Volume = 94.two m³

Circular your answers to the nearest tenth if necessary. Use 3.fourteen for π.

Question 12.
Antonio is making mini waffle cones. Each waffle cone is 3 inches loftier and has a radius of \(\frac{three}{iv}\) inch. What is the book of a waffle cone?
_________ in³

Reply:
1.8 inⁱⁱⁱ

Explanation:
Radius = iii/4 in
Radius r = 0.75 in
Height = 3 in
Book of each waffle cone = 1/iii πr²h
Volume = i/3 (3.xiv) (0.75)² (three)
Volume = one.76625 in³
Volume = 1.eight in³

Question 13.
A snack bar sells popcorn in cone-shaped containers. One container has a diameter of 8 inches and a height of 10 inches. How many cubic inches of popcorn does the container hold?
_________ inⁱⁱⁱ

Respond:
167.five in³

Explanation:
Diameter of base of operations = eight in
Radius = 8/two in = 4 in
Height = 10 in
Volume of cone = 1/3 πr²h
Volume = i/3 (iii.fourteen) (iv)² (10)
Volume = 167.466 inⁱⁱⁱ
Book = 167.5 in³

Question 14.
A volcanic cone has a diameter of 300 meters and a height of 150 meters. What is the volume of the cone?
_________ mⁱⁱⁱ

Respond:
3534291.7 m³

Explanation:
Bore of base of operations = 300 m
Radius = 300/2 yard = 150 one thousand
Height = 150 m
Book of cone = 1/iii πr²h
Book = 1/three (3.14) (150)² (150)
Volume = 3534291.735 k³
Book = 3534291.7 m³

Question 15.
Multistep Orange traffic cones come in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone that has a top of two feet and a diameter of 10 inches. Use 3.xiv for π.
_________ in³

Reply:
628 in³

Explanation:
The radius of the cone is Bore/ii = 10/2 = 5
The height of the cone is 2 ft = 2 . 12 = 24 in
Vcone = 1/3 πr²h
Vcone = 1/3 (3.fourteen) (5)² (24)
Vcone = 628 in³

Find the missing measure for each cone. Round your answers to the nearest tenth if necessary. Use 3.fourteen for π.

Question sixteen.
radius = _______
height = 6 in.
volume = 100.48 in3
_________ in.

Respond:
radius = four in.
four in.

Explanation:
Allow radius be R.
Height = half dozen in
Volume = 100.4 in
Volume of cone = one/3 πr²h
√(3v/hπ) = R
√((3 × 100.48)/(18.84)) = R
√(301.44/xviii.84) = R
R = √(16)
R = 4 in

Question 17.
diameter = 6 cm
peak = _______
book = 56.52 cm³
_______ cm

Answer:
height = half-dozen cm
h = 6 cm

Explanation:
Permit height be h
Diameter = 6 cm
Radius = half-dozen/2 = 3 cm
Volume = 56.52 cm
Volume of cone = 1/3 πr²h
(3V/r²h) = h
(3 × 56.52)/(3² × 3.xiv) = h
169.56/28.26 = h
h = 6 cm

Question eighteen.
The diameter of a cone-shaped container is 4 inches, and its top is 6 inches. How much greater is the volume of a cylinder-shaped container with the same diameter and height? Round your answer to the nearest hundredth. Use 3.14 for π.
Type below:
____________

Reply:
The volume of the cylinder is 50.24 in³ greater than the volume of the cone.

Caption:
The diameter of a cone, d = 4 inch
radius of a cone, r = d/2 = 4/2 = 2 inches
acme of a cone, h = 6 inches.
So, book of a cone, V cone = 1/iii πr²h
= i/3 (3.14) (2)² (6)
= 25.12 in³
And volume of a cylinder with aforementioned diameter and height,
V cylinder = πr²h = (three.14) (2)² (six) = 75.36 in³
The volume of the cylinder is 50.24 in³ greater than the volume of the cone.

FOCUS ON College Guild THINKING – Volume of Cones – Folio No. 410

Question xix.
Alex wants to know the book of sand in an hourglass. When all the sand is in the lesser, he stands a ruler up beside the hourglass and estimates the peak of the cone of sand.
a. What else does he demand to measure out to find the book of sand?
____________

Answer:
To find the volume of the sand, he needs to measure the radius of the base of operations of the hourglass.

Question 19.
b. Make a Conjecture If the volume of sand is increasing at a constant charge per unit, is the peak increasing at a constant charge per unit? Explicate.
____________

Answer:
The volume of the cone is linearly proportional to the height of the cone. Therefore, if the volume is increasing at a abiding rate, the summit is also increasing at a constant rate.

Question 20.
Problem Solving The diameter of a cone is x cm, the height is 18 cm, and the volume is 301.44 cm³. What is 10? Use 3.xiv for π.
________ cm

Reply:
8 cm

Explanation:
V cone = 1/3 πr²h
301.44 = ane/3 . 3.14 . r² . 18
r² = 904.32/56.52
r² = xvi
r = four cm
The diameter of the circle is twice its radius, therefore
10 = ii . r
x = 2 . 4
x = eight cm

Question 21.
Analyze Relationships A cone has a radius of 1 foot and a acme of ii feet. How many cones of liquid would information technology take to fill a cylinder with a diameter of 2 feet and a height of 2 anxiety? Explain.
________ cones

Answer:
3 cones

Explanation:
The diameter of the base of operations of the cylinder is two anxiety, which means that its radius is 1 foot. Its height is 2 feet. The volume of this cylinder is
V cylinder = πr²h
V cylinder = (3.14) (1)² (2)
V cylinder = 6.28
The radius of the cone is 1 pes and the pinnacle of the cone is two feet. The volume of the cone is:
Five cone = one/3 πr²h
V cone = i/iii (three.xiv) (1)² (two)
Five cone = i/3 × half-dozen.28
V cone = one/3 . V cylinder
V cone = 2.09
It would accept 3 cones of liquid to fill the cylinder.

Question 22.
Critique Reasoning Herb knows that the volume of a cone is 1 third that of a cylinder with the aforementioned base and pinnacle. He reasons that a cone with the aforementioned height as a given cylinder simply 3 times the radius should therefore accept the same volume as the cylinder, since \(\frac{1}{3}\) ⋅ 3 = 1. Is Herb correct? Explain.
____________

Answer:
The volume of the given cylinder is 5 cylinder = πr²h
The volume of the cone with the same acme h equally a given cylinder but iii times the radius r is
V cone = 1/3 π(3r)²h
5 cone = 3 πr²h
5 cone = three V cylinder
Every bit we tin can see, Herb is not correct. The volume of the cone is non equal to the volume of the cylinder. But it is three times the volume of the cylinder.

Guided Practice – Book of Spheres – Page No. 414

Question 1.
Vocabulary A sphere is a three-dimensional effigy with all points _____ from the center.
Type below:
____________

Answer:
A sphere is a three-dimensional figure with all points at equal distance from the center.

Question 2.
Vocabulary The _____ is the distance from the eye of a sphere to a point on the sphere.
Type below:
____________

Respond:
radius

Explanation:
The radius is the altitude from the center f the sphere to a bespeak on the sphere

Discover the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question three.

_______ in^three

Answer:
iv.12 in³

Explanation:
5 = four/3πr³
V = 4/iii (iii.14) (1)³
V = 4.12 in³

Question 4.

_______ cm³

Answer:
4186.vii cm³

Caption:
Diameter = 20 cm
Radius r = 20/2 = 10 cm
Volume of sphere = 4/3πr³
Book = 4/3 (3.fourteen) (10)³
Volume = 4186.66 cm³
Book = 4186.7 cm³

Question five.
A sphere has a radius of 1.5 feet.
_______ ft³

Answer:
14.1 ft³

Caption:
Radius r = 1.5 ft
The volume of sphere = 4/3πr³
Volume = four/3 (3.xiv) (1.5)³
Volume = 14.13 ft³
Book = 14.1 ft³

Question vi.
A sphere has a diameter of 2 yards.
_______ yd³

Answer:
4.2 yd³

Caption:
Bore = two yards
Radius r = two/2 yards
Radius r = 1 yd
Volume of sphere = 4/3πr³
Volume = 4/3 (3.14) (one)³
Volume = 4.1866 yd³
Volume = 4.2 yd³

Question 7.
A baseball has a bore of 2.9 inches. Discover the book of the baseball. Circular your reply to the nearest tenth if necessary. Use 3.fourteen for π.
_______ in³

Respond:
12.8 in³

Caption:
Bore of baseball = 2.9 in
Radius r = ii.nine/2 in
Radius of baseball = 1.45 in
The volume of sphere = 4/3πr³
Book = 4/iii (3.14) (i.45)³
Book = 12.763 in³
Volume = 12.8 in³

Question viii.
A basketball game has a radius of 4.7 inches. What is its volume to the nearest cubic inch. Use three.14 for π.
_______ in³

Answer:
1304 in³

Explanation:
Radius of baseball = four.7 in
The volume of sphere = 4/3πr³
Volume = 4/three (3.14) (four.vii)³
Volume = 1304.0168 in³
Volume = 1304 in³

Question 9.
A company is deciding whether to package a ball in a cubic box or a cylindrical box. In either case, the ball will touch the bottom, summit, and sides.

a. What portion of the space inside the cylindrical box is empty? Explain.
Type below:
_______________

Answer:
The volume of the cylinder is 5 cylinder = πr²h
Since the ball touches the lesser, top, and sides, then the height of the cylinder will exist equal to 2r.
V cylinder = πr²(2r) = 2πr³
On the other manus, the volume of the sphere is
V sphere = iv/3 πr³
The volume of the empty space inside the cylindrical box is found by subtracting the volume of the sphere from the volume of the cylinder
5 cylinder – 5 sphere = 2πr³ – 4/3 πr³
= (2 – 4/3)πr³
= two/3πr³

Question 9.
b. Find an expression for the book of the cubic box.
Type beneath:
_______________

Answer:
The volume of a cube with side a is V cube = a³
Since the ball touches the bottom, acme, and sides, then the side of the cube will be equal to 2r.
V cube = (2r)³
Five cube = 8r³

Question 9.
c. Near what portion of the space inside the cubic box is empty? Explain
Blazon below:
_______________

Answer:
The volume of the empty space inside the cubical box is institute by subtracting the volume of the sphere from the volume of the cube:
V cube – 5 sphere = 8r³ – iv/3 πr³
= (8 – 4/3π)r³
= (8 – iv.2)r³
= 3.8r³

ESSENTIAL QUESTION CHECK-IN

Question 10.
Explain the steps you use to observe the volume of a sphere.
Type below:
_______________

Answer:
Pace 1: The radius of the sphere is plant out.
Stride 2: The volume of the sphere is 4/3 πr³; where R is the radius.
Step 3: Put the value of radius in the equation of volume.
Pace 4: Summate the volume.

thirteen.three Independent Practice – Volume of Spheres – Page No. 415

Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use three.14 for π.

Question 11.
radius of iii.1 meters
_______ grand³

Reply:
124.7 yard³

Caption:
The volume of the sphere with a radius of 3.1 meter is 4/three πr³
Five = 4/3 . (3.fourteen) . (three.one)³
V = 124.7 m³

Question 12.
diameter of 18 inches
_______ in³

Answer:
3052.1 in³

Explanation:
The diameter of the sphere is 18 inches, which ways that its radius is nine inches. The volume of the sphere is
Five = iv/iii πr³
V = four/3 . (3.14) . (9)³
Five = 3052.08 in³
V = 3052.1 in³

Question thirteen.
r = vi in.
_______ in³

Answer:
904.3 in³

Caption:
The volume of the sphere with a radius of 6 inches is
V = 4/iii πr³
V = 4/3 (3.xiv) (six)³
V = 904.32
V = 904.iii in³

Question fourteen.
d = 36 yard
_______ m³

Reply:
24416.half-dozen m³

Explanation:
d = 36 m
radius r = 36/2 = 18 yard
Volume = iv/3 πr³
= iv/iii (3.14) (eighteen)³
= 24416.64
Volume = 24416.half dozen m³

Question 15.

_______ cm³

Answer:
5572.5 cm³

Caption:
The volume of the sphere with a radius of 11 centimeters is
V = 4/iii πr³
V = 4/3 (3.14) (11)³
V = 5572.5 cm³

Question 16.

_______ ft^three

Answer:
8.two feet³

Explanation:
The diameter of the sphere is 2.five feet, which ways that its radius is 1.25 feet. The volume of the sphere is
V = iv/iii πr³
V = 4/3 . (3.14) . (one.25)³
Five = 8.2 feet³

The eggs of birds and other animals come in many dissimilar shapes and sizes. Eggs frequently have a shape that is nearly spherical. When this is true, y'all tin can use the formula for a sphere to detect their volume.

Question 17.
The green turtle lays eggs that are approximately spherical with an average bore of four.v centimeters. Each turtle lays an boilerplate of 113 eggs at once. Notice the total volume of these eggs, to the nearest cubic centimeter.
_______ cm³

Answer:
5389 cm³

Caption:
The bore of an egg (sphere) is 4.5 centimeters, which means that its radius is ii.25 centimeters. The volume of a single egg is
5 = 4/3 πr³
V = iv/3 (3.fourteen) (2.25)³
Five = 47.68875 cm³
Therefore, the total book of 113 eggs is
113 . V = 113(47.68875)
= 5388.82875
= 5389 cm³

Question xviii.
Hummingbirds lay eggs that are nearly spherical and about 1 centimeter in diameter. Discover the volume of an egg. Round your answer to the nearest 10th.
_______ cm³

Answer:
0.v cm³

Explanation:
The bore of an egg (sphere) is 1 centimeter, which means that its radius is 0.5 centimeters. The volume of a unmarried egg is
Five = four/3 πr³
5 = four/3 (3.14) (0.v)³
V = 0.v cm³

Question 19.
Fossilized spherical eggs of dinosaurs called titanosaurid sauropods were found in Patagonia. These eggs were fifteen centimeters in diameter. Detect the volume of an egg. Round your answer to the nearest tenth.
_______ cm³

Respond:
1766.25 cm³

Explanation:
Diameter of an egg = fifteen cm
Its radius = 15/2 = 7.5 cm
Book = 4/3 πr³
V = 4/three (three.14) (vii.5)³
5 = 1766.25 cm³

Question xx.
Persevere in Trouble Solving An ostrich egg has about the same volume as a sphere with a diameter of 5 inches. If the eggshell is about \(\frac{i}{12}\) inch thick, notice the volume of but the shell, not including the interior of the egg. Round your reply to the nearest tenth.
_______ in³

Reply:
6.viii in³

Explanation:
Diameter including the eggshell
= five + (2 . 1/2)
= (5 + i/6) in
= 5.166 in
Radius including egg beat = 5.166/2 = two.5833 in
Volume = 4/iii πr³
Volume = 4/3 (three.14) (ii.5833)³
=72.176 in³
Volume with crush = 72.2 in³
Radius excluding trounce = 5/ii = ii.5 in
Volume = 4/3 (3.14) (2.five)³
= 65.416 in³
Volume (without beat) = 65.four in³
Volume of shell = Total volume – Inner Volume
= 72.two – 65.4
= half-dozen.8 in³

Question 21.
Multistep Write the steps you would use to find a formula for the book of the figure at right. And so write the formula.

Blazon below:
_____________

Answer:
5/3πr³

Explanation:
The radius of hemisphere = r
Radius of cylinder = r
Height of cylinder = r
Footstep 1: Find the formula for the volume of a hemisphere
The volume of hemisphere = 4/three π/ii r³
= 2/3πr³
Step 2: Detect the formula for the volume of a cylinder
The book of cylinder = πr²h
=πr³
Step 3: Add both the volume expressions:
Full volume = two/3πr³ + πr³
= 5/3πr³

Volume of Spheres – Page No. 416

Question 22.
Disquisitional Thinking Explain what happens to the volume of a sphere if y'all double the radius.
Type beneath:
_____________

Answer:
Let Radius = r
Volume V1 = iv/3πr³
Radius = 2r
Volume V2 = iv/3π(2r)³
= eight . 4/3πr³
= 8 V1
= eight(initial volume)
Past doubling the radius of sphere we brand the voulme eight times the intial value.

Question 23.
Multistep A cylindrical can of lawn tennis balls holds a stack of 3 balls so that they touch the tin at the top, bottom, and sides. The radius of each brawl is 1.25 inches. Detect the book inside the tin that is not taken upwardly past the three lawn tennis assurance.

_______ inⁱⁱⁱ

Respond:
12.3 in³

Caption:
Radius of the ball = 1.25 inch
Pinnacle of the cylinder = (2 × 1.25) × 3
= (2.five) × 3
= 7.5 in
radius of base of cylinder = i.25 in.
Volume of cylinder = πr²h
= (three.14) (i.25)² (seven.5)
= 36.7968
= 36.viii in³
Volume of a brawl (all three) = three × four/3πr³
= 4 (3.14) (1.25)³
= 24.53125 in³
= 24.5 in³
Volume of empty infinite = Book of cylinder – Volume of ball
= 36.8 – 24.5 = 12.3 in³

FOCUS ON College Club THINKING

Question 24.
Critique Reasoning A sphere has a radius of 4 inches, and a cube-shaped box has an border length of 7.5 inches. J.D. says the box has a greater volume, then the sphere will fit in the box. Is he correct? Explain.
_____________

Answer:
The book of sphere = iv/3πr³
= 4/3 (iii.fourteen) (four)³
= 267.9466
= 268
The volume of cube = (7.five)³
= 421.875
=421.9
The volume of cube > Book of a sphere
Just the base of the cube has an area of (seven.5 × seven.5) = 56.25 while the cross-action area of the sphere.
πr² = (3.14) (4)² = 50.24
The cantankerous-section area of the cube is less than that of a sphere. thus J.D. is wrong and the ball (sphere) will non fit in the cube.

Question 25.
Critical Thinking Which would hold the most water: a bowl in the shape of a hemisphere with radius r, a cylindrical glass with radius r and height r, or a cone-shaped drinking loving cup with radius r and elevation r? Explain.
_____________

Answer:
The volume of a sphere with radius r is
5 sphere = four/3πr³
Therefore, the book of a hemisphere is
V hemisphere = V sphere/two
V hemisphere = 2/3πr³
The volume of a cylinder with radius r and height r is
V cylinder = πr²h
V cylinder = πr³
The book of a cone with radius r and height r is
Five cone = one/3πr²h
Five cone = 1/3πr³
V cone < V hemisphere < Five cylinder
Therefore, the cylindrical glass with radius r and elevation r will hold the most water.

Question 26.
Analyze Relationships Hari has models of a sphere, a cylinder, and a cone. The sphere's bore and the cylinder's tiptop are the same, 2r. The cylinder has radius r. The cone has diameter 2r and height 2r. Compare the volumes of the cone and the sphere to the volume of the cylinder.
Type beneath:
_____________

Answer:
Radius of sphere = 2r/two = r
Volume of sphere = 4/3πr³
Radius of cylinder = r
Height of cylinder = 2r
volume of cylinder = πr²(2r)
V cylinder = 2πr³
Radius of cone = 2r/2 = r
Acme of cone = 2r
Book of cone = i/3 πr²(2r)
V cone = ii/3πr³
Volume of cylinder > Volume of sphere > Volume of cone
2πr³ > 4/3πr³ > 2/3πr³

Question 27.
A spherical helium balloon that is 8 feet in bore tin can lift about 17 pounds. What does the diameter of a balloon need to exist to lift a person who weighs 136 pounds? Explicate.
_______ feet

Answer:
Diameter of ballon = viii ft
Weight it could elevator = 17 pound
Volume = iv/iii π(8/2)³
= 4³(4π/three)
4³/10(4π/three) = 17/36
1/x = one/8 × 3/4π × 1/48
x = 4π/3 . four³ . ii³
ten = 4/3. π . viii³
The book of ballon which can lift 136 pounds is equal to 4/3. π . viii³
The radius of that ballon = 8ft
Diameter = 8 . ii = 16 ft

Ready to Go along ? – Model Quiz – Page No. 417

13.1 Book of Cylinders

Find the book of each cylinder. Round your answers to the nearest tenth if necessary. Employ 3.14 for π.

Question ane.

_______ ft³

Answer:
904.8 ft³

Explanation:
Radius of base = six ft
Height of cylinder = viii ft
The volume of cylinder = πr²h
Volume = (three.14) (half dozen)² (8)
Volume = 904.77 ft³
Volume = 904.viii ft³

Question 2.
A can of juice has a radius of 4 inches and a top of seven inches. What is the volume of the tin can?
_______ in³

Respond:
351.7 in³

Explanation:
Radius if cylindrical can = 4 in
Tiptop of cylindrical can = vii in
The volume of cylinder = πr²h
Volume = (3.fourteen) (iv)² (vii)
Volume = 351.68 in³
Volume = 351.vii in³

13.2 Volume of Cones

Discover the volume of each cone. Round your answers to the nearest tenth if necessary. Utilize 3.14 for π.

Question three.

_______ cm³

Reply:
565.2 cm³

Explanation:
Radius of base of operations of cone = 6 cm
Height of cone = 15 cm
Volume of cone = ane/3πr²h
Volume = i/iii (iii.14) (4)² (7)
Volume = 565.2 cm³

Question 4.

_______ in³

Reply:
3014.4 in³

Caption:
The radius of the base of cone = 12 in
Elevation of cone = xx in
The volume of cone = 1/3πr²h
Volume = 1/3 (3.fourteen) (12)² (20)
Volume = 3014.iv in³

13.iii Volume of Spheres

Observe the book of each sphere. Round your answers to the nearest tenth if necessary. Use three.14 for π.

Question 5.

_______ in³

Reply:
113 in³

Caption:
Radius of sphere = 3 ft
Book of sphere = 4/3πr³
Volume = 4/3 (3.14) (iii)³
Volume = 113.04 ft³
Volume = 113 in³

Question six.

_______ cmⁱⁱⁱ

Answer:
1149.8 cm³

Explanation:
Diameter = 13 cm
Radius = xiii/2 cm = 6.5 cm
Volume of sphere = 4/3πr³
Volume = 4/three (3.14) (6.five)³
Volume = 1149.7633 cm³
Volume = 1149.8 cm³

ESSENTIAL QUESTION

Question 7.
What measurements do you need to know to notice the volume of a cylinder? a cone? a sphere?
Type beneath:
___________

Answer:
Sphere: To find the book of the sphere, the radius is to exist measured.
Cylinder: To mensurate the book of the cylinder, we need to find out the base radius of the base of the cylinder forth with the superlative of the cylinder.
Cone: To summate the volume of the cone, we demand to summate the base of operations radius of the base of the cone along with the height of the cone.

Explanation:
The book of sphere = 4/iii πr³
Sphere: For finding the volume of the sphere, the radius is to exist measured
The volume of Cylinder = πr²h
Cylinder: To calculate the volume of the cylinder, we demand to find out the base radius of the base of the cylinder forth with the height of the cylinder
The volume of Cone = 1/3 πr²h
Cone: To calculate the book of the cone, we need to measure the base of operations radius of the base of the cone along with the height of the cone

Selected Response – Mixed Review – Page No. 418

Question ane.
The bed of a pickup truck measures 4 feet past 8 feet. To the nearest inch, what is the length of the longest thin metallic bar that will lie flat in the bed?
Options:
a. 11 ft three in.
b. 10 ft 0 in.
c. 8 ft xi in.
d. viii ft nine in.

Reply:
d. 8 ft 9 in.

Explanation:
The length of the longest thin metal bar that volition lie flat in the bed's equal to the length of the bed's hypotenuse. Let a = 4 and b = 8. Using the Pythagorean Theorem
a² + b² = c²
4² + 8² = c²
16 + 64 = c²
80 = c²
Rounding the length of the hypotenuse to the nearest tenth of a foot
c = 8.nine ft
Therefore, the length of the longest thin metal bar that volition prevarication flat in the bed is 8 ft. 9 in.

Question 2.
Using 3.14 for π, what is the volume of the cylinder beneath to the nearest tenth?

OPtions:
a. 102 cubic yards
b. 347.half dozen cubic yards
c. 1,091.six cubic yards
d. 4,366.4 cubic yards

Answer:
c. 1,091.6 cubic yards

Explanation:
Diameter of the base of operations of the cylinder = 11.four yd
Radius = xi.four/2 yd = 5.vii yd
Acme = x.7 ys
Volume of cylinder = πr²h
Volume = (3.14) (5.vii)² (10.seven)
Volume = 1091.599 yd³
Volume = 1091.vi yd³

Question 3.
Rhett fabricated mini waffle cones for a birthday party. Each waffle cone was 3.5 inches high and had a radius of 0.viii inches. What is the volume of each cone to the nearest hundredth?
Options:
a. 1.70 cubic inches
b. 2.24 cubic inches
c. 2.34 cubic inches
d. eight.79 cubic inches

Respond:
c. 2.34 cubic inches

Explanation:
Superlative of each waffle cone = 3.5 in
Radius of base = 0.8 in
Book of cone = 1/3 πr²h
Book = i/three (three.14) (0.eight)² (three.5)
Volume = two.344533 in³
Book = ii.34 in³

Question 4.
What is the volume of a cone that has a height of 17 meters and a base of operations with a radius of 6 meters? Utilise 3.14 for π and round to the nearest 10th.
Options:
a. 204 cubic meters
b. 640.6 cubic meters
c. 2,562.2 cubic meters
d. 10,249 cubic meters

Answer:
b. 640.6 cubic meters

Explanation:
Height of the cone = 17 one thousand
Radius of base = half dozen m
Book of cone = 1/3 πr²h
Volume = ane/iii (3.14) (6)² (17)
Volume = 640.56 k³
Volume = 640.6 1000³

Question 5.
Using 3.14 for π, what is the volume of the sphere to the nearest 10th?

Options:
a. four,180 cubic centimeters
b. five,572.5 cubic centimeters
c. 33,434.7 cubic centimeters
d. 44,579.6 cubic centimeters

Respond:
b. 5,572.five cubic centimeters

Explanation:
Diameter of the base of operations of the sphere = 22 cm
Radius = 22/2 yd = xi cm
Volume of sphere = 4/3 πr³
Volume = four/3 (three.xiv) (11)³
Book = 5572.4533 cm³
Volume = 5572.5 cm³

Mini-Task

Question 6.
A diagram of a deodorant container is shown. It is fabricated upwards of a cylinder and half of a sphere.

Use 3.14 for π and round answers to the nearest 10th.
a. What is the volume of the half sphere?
_______ cm³

Answer:
8.574 cm³

Caption:
The radius of the cylinder every bit well as the hemisphere = one.half-dozen cm
Height = 6.2 cm
the volume of the hemisphere = 2/iii πr³
the volume of the hemisphere = ii/3 (three.14) (1.six)³
the volume of the hemisphere = 8.574 cm³

Question 6.
b. What is the volume of the cylinder?
_______ cmⁱⁱⁱ

Answer:
49.838 cm³

Explanation:
The book of cylinder = πr²h
= (3.14) (i.half-dozen)² (6.2)
= 49.838 cm³

Question 6.
c. What is the volume of the whole figure?
_______ cm³

Answer:
58.iv cm³

Explanation:
Total volume = Volume of cylinder + volume of a hemisphere
Total volume = 8.574 cm³ + 49.838 cm³
Total volume = 58.4 cm³

Conclusion:

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