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Geometry Tutor
Worksheet 19
Cylinders, Cones,
and
Spheres
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Geometry Tutor - Worksheet 19 – Cylinders, Cones, and Spheres
1. What are the approximate volume and surface area of a sphere that has a
diameter of 12 m? Round your answer to the nearest hundredth.
2. What are the exact volume and surface area of a sphere that has a radius of
5√7 cm?
3. A sphere has a volume of 972𝜋 mm3. What are the exact radius and surface
area of the sphere?
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4. A sphere has a surface area of 144𝜋 m2. What are the exact radius and volume
of the sphere?
5. What are the approximate surface area and volume of this sphere? Round your
answer to the nearest hundredth.
6. What are the approximate surface area and volume of this sphere?
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7. What are the approximate surface area and volume of this sphere? Round your
answer to the nearest hundredth.
8. What are the approximate surface area and volume of this sphere? Round your
answer to the nearest hundredth.
9. What are the exact surface area and volume of this sphere?
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10. What are the approximate volume and surface area of a cylinder that has a
diameter of 24 𝑐m and a height of 8 cm?
11. What are the exact volume and surface area of a cylinder that has a radius of
2√3 cm and a height of 8√3 cm?
12. A cylinder has a volume of 576𝜋 dm3 and a height of 9 dm. What is the exact
radius of the cylinder?
13. A cylinder has a surface area of 88𝜋 m2 and a radius of 4 m. What are the
exact radius and volume of the cylinder?
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14. What are the approximate volume and surface area of this cylinder?
15. What is the exact surface area of this cylinder?
16. What is the approximate volume of this cylinder?
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17. What is the approximate surface area of this cylinder?
18. What is the exact volume of this cylinder?
19. What are the exact volume and surface area of this cylinder?
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20. A cone has a volume of 168𝜋 hm3 and a radius of 6 hm. What is the exact
height of the cone?
21. A cone has a volume of 459𝜋 cm3 and a height of 17 cm. What is the exact
radius of the cone?
22. What is the exact volume of this cone?
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23. What is the approximate volume of this cone? Round your answer to the
nearest hundredth.
24. What is the exact volume of this cone?
25. What is the approximate volume of this cone?
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26. What is the exact volume of this cone?
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Answers - Geometry Tutor - Worksheet 19 – Cylinders, Cones, and Spheres
1. What are the approximate volume and surface area of a sphere that has a
diameter of 12 m? Round your answer to the nearest hundredth.
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number with a value of 3.14 when estimating, and 𝑟 is the radius of
the sphere. The diameter is twice the radius. The volume is
𝑉 =4
3(3.14)(6 m)3 = 904.32 m3
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number with a value of 3.14 when estimating, and 𝑟 is the radius
of the sphere. The diameter is twice the radius. The surface area is
𝐴 = 4(3.14)(6 m)2 = 452.16 m2
Answer: Volume: 904.32 m3 Surface Area: 452.16 m2
2. What are the exact volume and surface area of a sphere that has a radius of
5√7 cm?
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3𝜋(5√7 cm)3 =
3500𝜋√7
3 cm3
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number, and 𝑟 is the radius of the sphere. The surface area is
𝐴 = 4𝜋(5√7 cm)2 = 700𝜋 cm2
Answer: Volume: 3500𝜋√7
3 cm3 Surface Area: 700𝜋 cm2
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3. A sphere has a volume of 972𝜋 mm3. What are the exact radius and surface
area of the sphere?
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. Use the volume formula
972𝜋 mm3 =4
3𝜋(𝑟 mm)3
972𝜋 mm3 =4
3𝜋(𝑟3) mm3
972 =4
3𝑟3
729 = 𝑟3
𝑟 = 9 mm
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number, and 𝑟 is the radius of the sphere. The surface area is
𝐴 = 4𝜋(9 mm)2 = 4𝜋(81) mm2 = 324𝜋 mm2
Answer: radius: 9 mm Surface Area: 324𝜋 mm2
4. A sphere has a surface area of 144𝜋 m2. What are the exact radius and volume
of the sphere?
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number, and 𝑟 is the radius of the sphere. Use the surface area
formula:
144𝜋 m2 = 4𝜋(𝑟 m)2
144𝜋 m2 = 4𝜋(𝑟2) m2
144 = 4𝑟2
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36 = 𝑟2
𝑟 = 6 m
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3𝜋(6 m)3 =
4
3𝜋(216) m3 = 288𝜋 m3
Answer: Radius: 6 m Volume: 288𝜋 m3
5. What are the approximate surface area and volume of this sphere? Round your
answer to the nearest hundredth.
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number with a value of 3.14 when estimating, and 𝑟 is the radius
of the sphere. The diameter is twice the radius. The surface area is:
𝐴 = 4(3.14)(7.8 mm)2
𝐴 = 4(3.14)(60.84) mm2
𝐴 = 764.1504 mm2
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3(3.14)(7.8 mm)3 =
4
3(3.14)(474.552) mm3 = 1986.79104 mm3
Answer: Surface Area: 764.15 mm2 Volume: 1986.79 mm3
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6. What are the approximate surface area and volume of this sphere?
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number with a value of 3.14 when estimating, and 𝑟 is the radius
of the sphere. The surface area is:
𝐴 = 4(3.14)(15 cm)2
𝐴 = 4(3.14)(225) cm2
𝐴 = 2826 cm2
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3(3.14)(15 cm)3 =
4
3(3.14)(3375) cm3 = 14130 cm3
Answer: Surface Area: 2826 cm2 Volume: 14130 cm3
7. What are the approximate surface area and volume of this sphere? Round your
answer to the nearest hundredth.
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The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number with a value of 3.14 when estimating, and 𝑟 is the radius
of the sphere. The diameter is twice the radius. The surface area is:
𝐴 = 4(3.14)(16.4 cm)2
𝐴 = 4(3.14)(268.96) cm2
𝐴 = 3378.1376 cm2
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3(3.14)(16.4 cm)3 =
4
3(3.14)(4410.944) cm3 = 18467.15221 cm3
Answer: Surface Area: 3378.14 cm2 Volume: 18467.15 cm3
8. What are the approximate surface area and volume of this sphere? Round your
answer to the nearest hundredth.
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number with a value of 3.14 when estimating, and 𝑟 is the radius
of the sphere. The diameter is twice the radius. The surface area is:
𝐴 = 4(3.14)(4.3 mm)2
𝐴 = 4(3.14)(18.49) mm2
𝐴 = 232.2344 mm2
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The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3(3.14)(4.3 mm)3 =
4
3(3.14)(79.507) mm3 = 332.8693067 mm3
Answer: Surface Area: 232.23 mm2 Volume: 332.87 mm3
9. What are the exact surface area and volume of this sphere?
The formula for the surface area of a sphere is 𝐴 = 4𝜋𝑟2 𝐴 is the surface area, 𝜋
is an irrational number, and 𝑟 is the radius of the sphere. The surface area is:
𝐴 = 4𝜋(25 dm)2
𝐴 = 4𝜋(625) dm2
𝐴 = 2500𝜋 dm2
The formula for the volume of a sphere is 𝑉 =4
3𝜋𝑟3 where 𝑉 is the volume, 𝜋 is
an irrational number, and 𝑟 is the radius of the sphere. The volume is
𝑉 =4
3𝜋(25 dm)3 =
4
3𝜋(15625) dm3 =
62500𝜋
3 dm3
Answer: Surface Area: 2500𝜋 dm2 Volume: 62500𝜋
3 dm3
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10. What are the approximate volume and surface area of a cylinder that has a
diameter of 24 𝑐m and a height of 8 cm?
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number with a value of 3.14 when estimating, 𝑟 is the
radius, and ℎ is the height. The diameter is twice the radius. The volume is
𝑉 = (3.14)(12 cm)2(8 cm)
𝑉 = (3.14)(144)(8)cm3
𝑉 = 3617.28 cm3
The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number with a value of 3.14 when estimating, 𝑟 is
the radius, and ℎ is the height. The diameter is twice the radius. The surface area
is
𝐴 = 2(3.14)(12 cm)2 + 2(3.14)(12 cm)(8 cm)
𝐴 = 2(3.14)(144) cm2 + 2(3.14)(12)(8) cm2
𝐴 = 904.32 cm2 + 602.88 cm2
𝐴 = 1507.2 cm2
Answer: Volume: 3617.28 cm3 Surface Area: 1507.2 cm2
11. What are the exact volume and surface area of a cylinder that has a radius of
2√3 cm and a height of 8√3 cm?
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
diameter is twice the radius. The volume is
𝑉 = 𝜋(2√3 cm)2
(8√3 cm)
𝑉 = 𝜋(12)(8√3)cm3
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𝑉 = 96𝜋√3 cm3
The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number with a value of 3.14 when estimating, 𝑟 is
the radius, and ℎ is the height. The surface area is
𝐴 = 2𝜋(2√3 cm)2 + 2𝜋(2√3 cm)(8√3 cm)
𝐴 = 2𝜋(12) cm2 + 2𝜋(2√3)(8√3) cm2
𝐴 = 24𝜋 cm2 + 96𝜋 cm2
𝐴 = 120𝜋 cm2
Answer: Volume: 96𝜋√3 cm3 Surface Area: 120𝜋 cm2
12. A cylinder has a volume of 576𝜋 dm3 and a height of 9 dm. What is the exact
radius of the cylinder?
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. Use the
volume formula to find 𝑟.
576𝜋 dm3 = 𝜋( dm)2(9 dm)
576𝜋 dm3 = 9𝜋𝑟2 dm3
576 = 9𝑟2
64 = 𝑟2
𝑟 = 8 dm
Answer: 8 dm
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13. A cylinder has a surface area of 88𝜋 m2 and a radius of 4 m. What are the
exact radius and volume of the cylinder?
The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. Use the
surface area formula to find 𝑟
88𝜋 m2 = 2𝜋(4 m)2 + 2𝜋(4 m)(ℎ m)
88𝜋 m2 = 32𝜋 m2 + 8𝜋ℎ m2
88 = 32 + 8ℎ
56 = 8ℎ
ℎ = 7 m
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
diameter is twice the radius. The volume is
𝑉 = 𝜋(4 m)2(7 m)
𝑉 = 𝜋(16)(7)m3
𝑉 = 112𝜋 m3
Answer: Radius: 7 m Volume: 112𝜋 m3
14. What are the approximate volume and surface area of this cylinder?
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The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
diameter is twice the radius. The volume is
𝑉 = (3.14)(7 dam)2(8 dam)
𝑉 = (3.14)(49)(8) dam3
𝑉 = 1230.88 dam3
The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number with a value of 3.14 when estimating, 𝑟 is
the radius, and ℎ is the height. The surface area is
𝐴 = 2(3.14)(7 dam)2 + 2(3.14)(7 dam)(8 dam)
𝐴 = 2(3.14)(49) dam2 + 2(3.14)(7)(8) dam2
𝐴 = 307.72 dam2 + 351.68 dam2
𝐴 = 659.4 dam2
Answer: Volume: 1230.88 dam3 Surface Area: 659.4 dam2
15. What is the exact surface area of this cylinder?
The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number with a value of 3.14 when estimating, 𝑟 is
the radius, and ℎ is the height. The surface area is
𝐴 = 2𝜋(5 cm)2 + 2𝜋(5 cm)(4 cm)
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𝐴 = 2𝜋(25) cm2 + 2𝜋(5)(4) cm2
𝐴 = 50𝜋 cm2 + 40𝜋 cm2
𝐴 = 90𝜋 cm2
Answer: 90𝜋 cm2
16. What is the approximate volume of this cylinder?
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
diameter is twice the radius. The volume is
𝑉 = (3.14)(14 m)2(16 m)
𝑉 = (3.14)(196)(16) m3
𝑉 = 9847.04 m3
Answer: 9847.04 m3
17. What is the approximate surface area of this cylinder?
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The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number with a value of 3.14 when estimating, 𝑟 is
the radius, and ℎ is the height. The diameter is twice the radius. The surface area
is
𝐴 = 2(3.14)(33 m)2 + 2(3.14)(33 m)(33 m)
𝐴 = 2(3.14)(1089) m2 + 2(3.14)(33)(33) m2
𝐴 = 6838.92 m2 + 6838.92 m2
𝐴 = 13677.84 m2
Answer: 13677.84 m2
18. What is the exact volume of this cylinder?
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
diameter is twice the radius. The volume is
𝑉 = 𝜋(4 m)2(7 m)
𝑉 = 𝜋(16)(7)m3
𝑉 = 112𝜋 m3
Answer: 112𝜋 m3
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19. What are the exact volume and surface area of this cylinder?
The formula for calculating the volume of a cylinder is 𝑉 = 𝜋𝑟2ℎ where 𝑉 is the
volume, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
diameter is twice the radius. The volume is
𝑉 = 𝜋(2 cm)2(12 cm)
𝑉 = 𝜋(4)(12)cm3
𝑉 = 48𝜋 cm3
The formula for the surface area of a cylinder is 𝐴 = 2𝜋𝑟2 + 2𝜋𝑟ℎ where 𝐴 is the
surface area, 𝜋 is an irrational number, 𝑟 is the radius, and ℎ is the height. The
surface area is
𝐴 = 2𝜋(2 cm)2 + 2𝜋(2 cm)(12 cm)
𝐴 = 2𝜋(4) cm2 + 2𝜋(2)(12) cm2
𝐴 = 8𝜋 cm2 + 48𝜋 cm2
𝐴 = 56𝜋 cm2
Answer: Volume: 48𝜋 cm3 Surface Area: 56𝜋 cm2
20. A cone has a volume of 168𝜋 hm3 and a radius of 6 hm. What is the exact
height of the cone?
The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number, 𝑟 is the radius of the base, and ℎ is the height of the cone. Use
the volume formula to find the height.
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168𝜋 hm3 =1
3𝜋(6 hm)2(ℎ hm)
168𝜋 hm3 =1
3𝜋(36)(ℎ) hm3
168 =1
3(36ℎ)
168 = 12ℎ
ℎ = 14 hm
Answer: 14 hm
21. A cone has a volume of 459𝜋 cm3 and a height of 17 cm. What is the exact
radius of the cone?
The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number, 𝑟 is the radius of the base, and ℎ is the height of the cone. Use
the volume formula to find the height.
459𝜋 cm3 =1
3𝜋(𝑟 cm)2(17 cm)
459𝜋 cm3 =1
3𝜋(𝑟2)(17) cm3
459 =1
3(17𝑟2)
1377 = 17𝑟2
81 = 𝑟2
𝑟 = 9 cm
Answer: 9 cm
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22. What is the exact volume of this cone?
The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number, 𝑟 is the radius of the base, and ℎ is the height of the cone. The
volume is
𝑉 =1
3𝜋(13 dm)2(30 dm)
𝑉 =1
3𝜋(169)(30) dm3
𝑉 =1
3𝜋(5070) dm3
𝑉 = 1690𝜋 dm3
Answer: 1690𝜋 dm3
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23. What is the approximate volume of this cone? Round your answer to the
nearest hundredth.
The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number with a value of 3.14 when estimating, 𝑟 is the radius of the
base, and ℎ is the height of the cone. The diameter is twice the radius. The
volume is
𝑉 =1
3(3.14)(7.15 m)2(9.6 m)
𝑉 =1
3(3.14)(51.1225)(9.6) m3
𝑉 = 513.67888 m3
Answer: 513.68 m3
24. What is the exact volume of this cone?
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The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number, 𝑟 is the radius of the base, and ℎ is the height of the cone. The
diameter is twice the radius. The volume is
𝑉 =1
3𝜋(9 m)2(18 m)
𝑉 =1
3𝜋(81)(18) m3
𝑉 = 486𝜋 m3
Answer: 486𝜋 m3
25. What is the approximate volume of this cone?
The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number with a value of 3.14 when estimating, 𝑟 is the radius of the
base, and ℎ is the height of the cone. The volume is
𝑉 =1
3(3.14)(3 hm)2(17 hm)
𝑉 =1
3(3.14)(9)(17) hm3
𝑉 = 160.14 hm3
Answer: 160.14 hm3
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26. What is the exact volume of this cone?
The formula for calculating the volume of a cone is 𝑉 =1
3𝐵ℎ =
1
3𝜋𝑟2ℎ where 𝑉 is
the volume, 𝐵 is the area of the base (which is always a circle in a cone), 𝜋 is an
irrational number, 𝑟 is the radius of the base, and ℎ is the height of the cone. The
diameter is twice the radius. The volume is
𝑉 =1
3𝜋(9 m)2(8 m)
𝑉 =1
3𝜋(81)(8) m3
𝑉 = 216𝜋 m3
Answer: 216𝜋 m3