Practice worksheet for calculating the volume of cylinders using given dimensions.

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:
- $ V $ = Volume
- $ B $ = Area of the base = $ \pi r^2 $
- $ r $ = Radius
- $ h $ = Height
- Use $ \pi \approx 3.14 $

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Problem 1

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

Work:
- $ B = \pi r^2 = 3.14 \times (2)^2 = 3.14 \times 4 = 12.56 $
- $ V = B \cdot h = 12.56 \times 5 = 62.8 $

Answers:
- Radius: 2 in
- Diameter: 4 in
- $ B = 12.56 $
- $ h = 5 $
- Volume: 62.8 in³

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Problem 2

Figure:
- Radius = 6 in (given as dotted line from center to edge)
- Length (height) = 8 in

Work:
- $ B = \pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 $
- $ V = B \cdot h = 113.04 \times 8 = 904.32 $

Answers:
- Radius: 6 in
- Diameter: 12 in
- $ B = 113.04 $
- $ h = 8 $
- Volume: 904.32 in³

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Problem 3

Figure:
- Diameter = 2 ft → Radius $ r = 1 $ ft
- Height = 7 in → Convert to feet? Wait, units differ.

Wait! The height is 7 inches, and diameter is 2 feet — inconsistent units.

Convert everything to inches:
- 2 ft = 24 inches → Radius = 12 inches
- Height = 7 inches

Now:
- $ r = 12 $ in
- $ h = 7 $ in

Work:
- $ B = \pi r^2 = 3.14 \times (12)^2 = 3.14 \times 144 = 452.16 $
- $ V = B \cdot h = 452.16 \times 7 = 3,165.12 $

Answers:
- Radius: 12 in
- Diameter: 24 in
- $ B = 452.16 $
- $ h = 7 $
- Volume: 3,165.12 in³

> Note: Units are mixed originally, but we converted feet to inches.

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Problem 4

Figure:
- Diameter = 2 in → Radius = 1 in
- Height = 4 in

Work:
- $ B = \pi r^2 = 3.14 \times (1)^2 = 3.14 $
- $ V = 3.14 \times 4 = 12.56 $

Answers:
- Radius: 1 in
- Diameter: 2 in
- $ B = 3.14 $
- $ h = 4 $
- Volume: 12.56 in³

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Problem 5

Figure:
- Diameter = 6 in → Radius = 3 in
- Height = 5 cm → Wait! Units are mixed again.

Diameter = 6 in, height = 5 cm → need consistent units.

Convert inches to cm or vice versa.

We'll convert inches to centimeters:
- 1 inch = 2.54 cm
- So 6 in = 6 × 2.54 = 15.24 cm → Radius = 7.62 cm
- Height = 5 cm

Now:
- $ r = 7.62 $ cm
- $ h = 5 $ cm

Work:
- $ B = \pi r^2 = 3.14 \times (7.62)^2 = 3.14 \times 58.0644 ≈ 182.32 $
- $ V = 182.32 \times 5 = 911.6 $

Answers:
- Radius: 7.62 cm
- Diameter: 15.24 cm
- $ B = 182.32 $
- $ h = 5 $
- Volume: 911.6 cm³

> Alternatively, if the problem intends both in inches, then height might be mislabeled. But since it says "5 cm", we assume that.

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Problem 6

Figure:
- Diameter = 8 in → Radius = 4 in
- Height = 10 in

Work:
- $ B = \pi r^2 = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 $
- $ V = 50.24 \times 10 = 502.4 $

Answers:
- Radius: 4 in
- Diameter: 8 in
- $ B = 50.24 $
- $ h = 10 $
- Volume: 502.4 in³

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✔ Final Answers Table:

| Problem | Radius | Diameter | B (Base Area) | h (Height) | Volume |
|--------|--------|----------|----------------|------------|--------|
| 1 | 2 in | 4 in | 12.56 | 5 in | 62.8 in³ |
| 2 | 6 in | 12 in | 113.04 | 8 in | 904.32 in³ |
| 3 | 12 in | 24 in | 452.16 | 7 in | 3,165.12 in³ |
| 4 | 1 in | 2 in | 3.14 | 4 in | 12.56 in³ |
| 5 | 7.62 cm | 15.24 cm | 182.32 | 5 cm | 911.6 cm³ |
| 6 | 4 in | 8 in | 50.24 | 10 in | 502.4 in³ |

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🔍 Notes:

- Always ensure units match before calculating.
- If not specified, assume all dimensions are in same unit.
- In Problem 5, the mix of inches and cm suggests possible typo — but we solved it correctly with conversion.

Let me know if you'd like this filled into the worksheet format!