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Geometry Tutor

Worksheet 19

Cylinders, Cones,

Spheres

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?

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?

9. What are the exact surface area and volume of this sphere?

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?

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?

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?

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?

23. What is the approximate volume of this cone? Round your answer to the

nearest hundredth.

25. What is the approximate volume of this cone?

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?

an irrational number, and 𝑟 is the radius of the sphere. The volume is

𝑉 =4

3𝜋(5√7 cm)3 =

3500𝜋√7

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

3. A sphere has a volume of 972𝜋 mm3. What are the exact radius and surface

area of the sphere?

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

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?

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

36 = 𝑟2

𝑟 = 6 m

𝑉 =4

3𝜋(6 m)3 =

3𝜋(216) m3 = 288𝜋 m3

Answer: Radius: 6 m Volume: 288𝜋 m3

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

𝑉 =4

3(3.14)(7.8 mm)3 =

3(3.14)(474.552) mm3 = 1986.79104 mm3

Answer: Surface Area: 764.15 mm2 Volume: 1986.79 mm3

6. What are the approximate surface area and volume of this sphere?

of the sphere. The surface area is:

𝐴 = 4(3.14)(15 cm)2

𝐴 = 4(3.14)(225) cm2

𝐴 = 2826 cm2

𝑉 =4

3(3.14)(15 cm)3 =

3(3.14)(3375) cm3 = 14130 cm3

Answer: Surface Area: 2826 cm2 Volume: 14130 cm3

𝐴 = 4(3.14)(16.4 cm)2

𝐴 = 4(3.14)(268.96) cm2

𝐴 = 3378.1376 cm2

𝑉 =4

3(3.14)(16.4 cm)3 =

3(3.14)(4410.944) cm3 = 18467.15221 cm3

Answer: Surface Area: 3378.14 cm2 Volume: 18467.15 cm3

𝐴 = 4(3.14)(4.3 mm)2

𝐴 = 4(3.14)(18.49) mm2

𝐴 = 232.2344 mm2

𝑉 =4

3(3.14)(4.3 mm)3 =

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?

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

𝑉 =4

3𝜋(25 dm)3 =

3𝜋(15625) dm3 =

62500𝜋

Answer: Surface Area: 2500𝜋 dm2 Volume: 62500𝜋

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

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?

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

𝑉 = 96𝜋√3 cm3

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?

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

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?

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

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?

𝑉 = (3.14)(7 dam)2(8 dam)

𝑉 = (3.14)(49)(8) dam3

𝑉 = 1230.88 dam3

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?

𝐴 = 2𝜋(5 cm)2 + 2𝜋(5 cm)(4 cm)

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?

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?

the radius, and ℎ is the height. The diameter is twice the radius. The surface area

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?

𝑉 = 𝜋(4 m)2(7 m)

𝑉 = 𝜋(16)(7)m3

𝑉 = 112𝜋 m3

Answer: 112𝜋 m3

19. What are the exact volume and surface area of this cylinder?

𝑉 = 𝜋(2 cm)2(12 cm)

𝑉 = 𝜋(4)(12)cm3

𝑉 = 48𝜋 cm3

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 =

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.

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?

3𝐵ℎ =

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

3𝐵ℎ =

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

23. What is the approximate volume of this cone? Round your answer to the

nearest hundredth.

3𝐵ℎ =

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

3𝐵ℎ =

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?

3𝐵ℎ =

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

3𝐵ℎ =

𝑉 =1

3𝜋(9 m)2(8 m)

𝑉 =1

3𝜋(81)(8) m3

𝑉 = 216𝜋 m3

Answer: 216𝜋 m3

geometry tutor worksheet 19 cylinders, cones, …...geometry tutor - worksheet 19 – cylinders,...

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