Volume of a Cylinder | Math Coach Amy

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What to Remember

Cylinder volume

The volume of a right cylinder is πr²h.

Square the radius, multiply by the height, and keep π.

Leave π

The answer stays in terms of π. Do not replace π with 3.14.

Use the radius

The formula uses the radius, which is the distance from the center to the edge.

Square that radius before you multiply by the height.

Level 1

Easy

The radius is 2, 3, 4, or 5.

Example

A right cylinder has radius 2 cm and height 5 cm. Find the volume in terms of π.

V = πr²h

V = π × 2² × 5

2² = 4

V = π × 4 × 5

V = 20π

Answer: 20π cubic cm

A right cylinder has radius 2 cm and height 3 cm. Find the volume in terms of π.

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V = πr²h

V = π × 2² × 3

2² = 4

V = π × 4 × 3

V = 12π

Answer: 12π cubic cm

A right cylinder has radius 2 in and height 4 in. Find the volume in terms of π.

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V = πr²h

V = π × 2² × 4

2² = 4

V = π × 4 × 4

V = 16π

Answer: 16π cubic in

A right cylinder has radius 2 ft and height 6 ft. Find the volume in terms of π.

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V = πr²h

V = π × 2² × 6

2² = 4

V = π × 4 × 6

V = 24π

Answer: 24π cubic ft

A right cylinder has radius 3 cm and height 2 cm. Find the volume in terms of π.

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V = πr²h

V = π × 3² × 2

3² = 9

V = π × 9 × 2

V = 18π

Answer: 18π cubic cm

A right cylinder has radius 3 in and height 4 in. Find the volume in terms of π.

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V = πr²h

V = π × 3² × 4

3² = 9

V = π × 9 × 4

V = 36π

Answer: 36π cubic in

A right cylinder has radius 3 ft and height 5 ft. Find the volume in terms of π.

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V = πr²h

V = π × 3² × 5

3² = 9

V = π × 9 × 5

V = 45π

Answer: 45π cubic ft

A right cylinder has radius 4 cm and height 2 cm. Find the volume in terms of π.

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V = πr²h

V = π × 4² × 2

4² = 16

V = π × 16 × 2

V = 32π

Answer: 32π cubic cm

A right cylinder has radius 4 in and height 3 in. Find the volume in terms of π.

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V = πr²h

V = π × 4² × 3

4² = 16

V = π × 16 × 3

V = 48π

Answer: 48π cubic in

A right cylinder has radius 5 ft and height 2 ft. Find the volume in terms of π.

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V = πr²h

V = π × 5² × 2

5² = 25

V = π × 25 × 2

V = 50π

Answer: 50π cubic ft

A right cylinder has radius 5 cm and height 3 cm. Find the volume in terms of π.

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V = πr²h

V = π × 5² × 3

5² = 25

V = π × 25 × 3

V = 75π

Answer: 75π cubic cm

Level 2

Medium

The radius is larger than 5.

Example

A right cylinder has radius 6 cm and height 4 cm. Find the volume in terms of π.

V = πr²h

V = π × 6² × 4

6² = 36

V = π × 36 × 4

V = 144π

Answer: 144π cubic cm

A right cylinder has radius 6 in and height 5 in. Find the volume in terms of π.

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V = πr²h

V = π × 6² × 5

6² = 36

V = π × 36 × 5

V = 180π

Answer: 180π cubic in

A right cylinder has radius 6 ft and height 3 ft. Find the volume in terms of π.

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V = πr²h

V = π × 6² × 3

6² = 36

V = π × 36 × 3

V = 108π

Answer: 108π cubic ft

A right cylinder has radius 7 cm and height 2 cm. Find the volume in terms of π.

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V = πr²h

V = π × 7² × 2

7² = 49

V = π × 49 × 2

V = 98π

Answer: 98π cubic cm

A right cylinder has radius 7 in and height 4 in. Find the volume in terms of π.

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V = πr²h

V = π × 7² × 4

7² = 49

V = π × 49 × 4

V = 196π

Answer: 196π cubic in

A right cylinder has radius 8 ft and height 3 ft. Find the volume in terms of π.

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V = πr²h

V = π × 8² × 3

8² = 64

V = π × 64 × 3

V = 192π

Answer: 192π cubic ft

A right cylinder has radius 8 cm and height 5 cm. Find the volume in terms of π.

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V = πr²h

V = π × 8² × 5

8² = 64

V = π × 64 × 5

V = 320π

Answer: 320π cubic cm

A right cylinder has radius 9 in and height 2 in. Find the volume in terms of π.

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V = πr²h

V = π × 9² × 2

9² = 81

V = π × 81 × 2

V = 162π

Answer: 162π cubic in

A right cylinder has radius 9 ft and height 4 ft. Find the volume in terms of π.

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V = πr²h

V = π × 9² × 4

9² = 81

V = π × 81 × 4

V = 324π

Answer: 324π cubic ft

A right cylinder has radius 10 cm and height 3 cm. Find the volume in terms of π.

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V = πr²h

V = π × 10² × 3

10² = 100

V = π × 100 × 3

V = 300π

Answer: 300π cubic cm

A right cylinder has radius 12 in and height 2 in. Find the volume in terms of π.

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V = πr²h

V = π × 12² × 2

12² = 144

V = π × 144 × 2

V = 288π

Answer: 288π cubic in

Level 3

Hard

The object is a right cylinder. Leave π in the volume.

Example

A soup can is a right cylinder. A right cylinder has radius 3 cm and height 10 cm. Find the volume in terms of π.

V = πr²h

V = π × 3² × 10

3² = 9

V = π × 9 × 10

V = 90π

Answer: 90π cubic cm

A cake is a right cylinder. A right cylinder has radius 4 in and height 6 in. Find the volume in terms of π.

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V = πr²h

V = π × 4² × 6

4² = 16

V = π × 16 × 6

V = 96π

Answer: 96π cubic in

A silo is a right cylinder. A right cylinder has radius 6 ft and height 20 ft. Find the volume in terms of π.

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V = πr²h

V = π × 6² × 20

6² = 36

V = π × 36 × 20

V = 720π

Answer: 720π cubic ft

A drum is a right cylinder. A right cylinder has radius 5 cm and height 8 cm. Find the volume in terms of π.

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V = πr²h

V = π × 5² × 8

5² = 25

V = π × 25 × 8

V = 200π

Answer: 200π cubic cm

A water tank is a right cylinder. A right cylinder has radius 8 ft and height 12 ft. Find the volume in terms of π.

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V = πr²h

V = π × 8² × 12

8² = 64

V = π × 64 × 12

V = 768π

Answer: 768π cubic ft

A candle is a right cylinder. A right cylinder has radius 2 in and height 7 in. Find the volume in terms of π.

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V = πr²h

V = π × 2² × 7

2² = 4

V = π × 4 × 7

V = 28π

Answer: 28π cubic in

A column is a right cylinder. A right cylinder has radius 3 ft and height 9 ft. Find the volume in terms of π.

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V = πr²h

V = π × 3² × 9

3² = 9

V = π × 9 × 9

V = 81π

Answer: 81π cubic ft

An oatmeal canister is a right cylinder. A right cylinder has radius 4 cm and height 10 cm. Find the volume in terms of π.

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V = πr²h

V = π × 4² × 10

4² = 16

V = π × 16 × 10

V = 160π

Answer: 160π cubic cm

A paint can is a right cylinder. A right cylinder has radius 5 in and height 6 in. Find the volume in terms of π.

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V = πr²h

V = π × 5² × 6

5² = 25

V = π × 25 × 6

V = 150π

Answer: 150π cubic in

A round cake pan is a right cylinder. A right cylinder has radius 9 in and height 5 in. Find the volume in terms of π.

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V = πr²h

V = π × 9² × 5

9² = 81

V = π × 81 × 5

V = 405π

Answer: 405π cubic in

A water tower is a right cylinder. A right cylinder has radius 10 ft and height 15 ft. Find the volume in terms of π.

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V = πr²h

V = π × 10² × 15

10² = 100

V = π × 100 × 15

V = 1500π

Answer: 1500π cubic ft

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