Finding Volume of Cylinders - Free Printable

Let's solve each cylinder volume problem step by step using the formula for the volume of a cylinder:

$$
V = B \cdot h = \pi r^2 h
$$

Where:
- $ r $ = radius of the base
- $ h $ = height of the cylinder
- $ B = \pi r^2 $ = area of the base
- Use $ \pi \approx 3.14 $

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Problem 1

Given:
- Diameter = 4 in → Radius $ r = \frac{4}{2} = 2 $ in
- Height $ h = 5 $ in

Calculations:
- Radius = 2 in
- Diameter = 4 in
- $ B = \pi r^2 = 3.14 \times (2)^2 = 3.14 \times 4 = 12.56 $
- $ h = 5 $
- Volume = $ B \cdot h = 12.56 \times 5 = 62.8 $ in³

✔ Answer:
- Radius: 2 in
- Diameter: 4 in
- B = 12.56
- h = 5
- Volume = 62.8 in³

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Problem 2

Given:
- Diameter = 6 in → Radius $ r = \frac{6}{2} = 3 $ in
- Height $ h = 8 $ in

Calculations:
- Radius = 3 in
- Diameter = 6 in
- $ B = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 $
- $ h = 8 $
- Volume = $ 28.26 \times 8 = 226.08 $ in³

✔ Answer:
- Radius: 3 in
- Diameter: 6 in
- B = 28.26
- h = 8
- Volume = 226.08 in³

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Problem 3

Given:
- Diameter = 2 ft → Radius $ r = \frac{2}{2} = 1 $ ft
- Height $ h = 7 $ ft

Note: Units are in feet.

Calculations:
- Radius = 1 ft
- Diameter = 2 ft
- $ B = 3.14 \times (1)^2 = 3.14 $
- $ h = 7 $
- Volume = $ 3.14 \times 7 = 21.98 $ ft³

✔ Answer:
- Radius: 1 ft
- Diameter: 2 ft
- B = 3.14
- h = 7
- Volume = 21.98 ft³

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Problem 4

Given:
- Diameter = 2 in → Radius $ r = 1 $ in
- Height $ h = 4 $ in

Calculations:
- Radius = 1 in
- Diameter = 2 in
- $ B = 3.14 \times (1)^2 = 3.14 $
- $ h = 4 $
- Volume = $ 3.14 \times 4 = 12.56 $ in³

✔ Answer:
- Radius: 1 in
- Diameter: 2 in
- B = 3.14
- h = 4
- Volume = 12.56 in³

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Problem 5

Given:
- Diameter = 6 in → Radius $ r = 3 $ in
- Height $ h = 5 $ in

Calculations:
- Radius = 3 in
- Diameter = 6 in
- $ B = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 $
- $ h = 5 $
- Volume = $ 28.26 \times 5 = 141.3 $ in³

✔ Answer:
- Radius: 3 in
- Diameter: 6 in
- B = 28.26
- h = 5
- Volume = 141.3 in³

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Problem 6

Given:
- Diameter = 8 in → Radius $ r = 4 $ in
- Height $ h = 10 $ in

Calculations:
- Radius = 4 in
- Diameter = 8 in
- $ B = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 $
- $ h = 10 $
- Volume = $ 50.24 \times 10 = 502.4 $ in³

✔ Answer:
- Radius: 4 in
- Diameter: 8 in
- B = 50.24
- h = 10
- Volume = 502.4 in³

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✔ Final Answers Summary:

| Problem | Radius | Diameter | B | h | Volume |
|--------|--------|----------|---------|-----|------------|
| 1 | 2 in | 4 in | 12.56 | 5 | 62.8 in³ |
| 2 | 3 in | 6 in | 28.26 | 8 | 226.08 in³ |
| 3 | 1 ft | 2 ft | 3.14 | 7 | 21.98 ft³ |
| 4 | 1 in | 2 in | 3.14 | 4 | 12.56 in³ |
| 5 | 3 in | 6 in | 28.26 | 5 | 141.3 in³ |
| 6 | 4 in | 8 in | 50.24 | 10 | 502.4 in³ |

> 🔍 Note: Always remember to use consistent units and double-check whether you're given diameter or radius! The formula uses radius, so convert diameter to radius by dividing by 2.

Let me know if you'd like this as a printable filled-in worksheet!