Let's solve each problem step by step using the formula for the
volume of a cylinder:
$$
V = \pi r^2 h
$$
We'll use $ \pi \approx 3.14 $, and round answers to the nearest tenth.
---
Problem 1
- Radius $ r = 5 $ mm
- Height $ h = 6 $ mm
$$
V = 3.14 \times (5)^2 \times 6 = 3.14 \times 25 \times 6 = 3.14 \times 150 = 471.0 \text{ mm}^3
$$
✔ Answer: 471.0 mm³
---
Problem 2
- Radius $ r = 3 $ m
- Height $ h = 6 $ m
$$
V = 3.14 \times (3)^2 \times 6 = 3.14 \times 9 \times 6 = 3.14 \times 54 = 169.56 \approx 169.6 \text{ m}^3
$$
✔ Answer: 169.6 m³
---
Problem 3
- Radius $ r = 3 $ cm
- Height $ h = 9 $ cm
$$
V = 3.14 \times (3)^2 \times 9 = 3.14 \times 9 \times 9 = 3.14 \times 81 = 254.34 \approx 254.3 \text{ cm}^3
$$
✔ Answer: 254.3 cm³
---
Problem 4
- Radius $ r = 5 $ cm
- Height $ h = 12 $ cm
$$
V = 3.14 \times (5)^2 \times 12 = 3.14 \times 25 \times 12 = 3.14 \times 300 = 942.0 \text{ cm}^3
$$
✔ Answer: 942.0 cm³
---
Problem 5
- Radius $ r = 7 $ mm
- Height $ h = 8 $ mm
$$
V = 3.14 \times (7)^2 \times 8 = 3.14 \times 49 \times 8 = 3.14 \times 392 = 1230.88 \approx 1230.9 \text{ mm}^3
$$
✔ Answer: 1230.9 mm³
---
Problem 6
- Radius $ r = 1 $ m
- Height $ h = 10 $ m
$$
V = 3.14 \times (1)^2 \times 10 = 3.14 \times 1 \times 10 = 31.4 \text{ m}^3
$$
✔ Answer: 31.4 m³
---
✔ Final Answers:
1.
471.0 mm³
2.
169.6 m³
3.
254.3 cm³
4.
942.0 cm³
5.
1230.9 mm³
6.
31.4 m³
---
💡
Explanation Summary:
To find the volume of a cylinder:
1. Square the radius ($ r^2 $).
2. Multiply by $ \pi $ (use 3.14).
3. Multiply by the height ($ h $).
4. Round to the nearest tenth.
This works regardless of orientation — cylinders can be upright or tilted; only the radius and height matter.
Parent Tip: Review the logic above to help your child master the concept of volume of a cylinder worksheet.
