Let's solve each cylinder volume problem step by step using the
formula for the volume of a cylinder:
$$
V = \pi r^2 h
$$
Where:
- $ V $ is the volume,
- $ r $ is the radius of the base,
- $ h $ is the height (or length) of the cylinder,
- $ \pi \approx 3.14 $ or use $ \frac{22}{7} $ if exact form is needed.
We’ll compute the volume for each cylinder, using
exact values where possible (in terms of $ \pi $), unless otherwise specified.
---
1)
- Diameter = 6 m → Radius $ r = 3 $ m
- Height $ h = 12 $ m
$$
V = \pi (3)^2 (12) = \pi \cdot 9 \cdot 12 = 108\pi \text{ m}^3
$$
✔ Volume = $ 108\pi $ m³
---
2)
- Diameter = 8 ft → Radius $ r = 4 $ ft
- Length (height) = 15 ft
$$
V = \pi (4)^2 (15) = \pi \cdot 16 \cdot 15 = 240\pi \text{ ft}^3
$$
✔ Volume = $ 240\pi $ ft³
---
3)
- Diameter = 10 cm → Radius $ r = 5 $ cm
- Height = 6 cm
$$
V = \pi (5)^2 (6) = \pi \cdot 25 \cdot 6 = 150\pi \text{ cm}^3
$$
✔ Volume = $ 150\pi $ cm³
---
4)
- Diameter = 6 m → Radius $ r = 3 $ m
- Height = 5 m
$$
V = \pi (3)^2 (5) = \pi \cdot 9 \cdot 5 = 45\pi \text{ m}^3
$$
✔ Volume = $ 45\pi $ m³
---
5)
- Diameter = 7 ft → Radius $ r = 3.5 $ ft
- Height = 12 ft
$$
V = \pi (3.5)^2 (12) = \pi \cdot 12.25 \cdot 12 = 147\pi \text{ ft}^3
$$
✔ Volume = $ 147\pi $ ft³
---
6)
- Diameter = 8 mm → Radius $ r = 4 $ mm
- Height = 8 mm
$$
V = \pi (4)^2 (8) = \pi \cdot 16 \cdot 8 = 128\pi \text{ mm}^3
$$
✔ Volume = $ 128\pi $ mm³
---
7)
- Diameter = 11 cm → Radius $ r = 5.5 $ cm
- Height = 10 cm
$$
V = \pi (5.5)^2 (10) = \pi \cdot 30.25 \cdot 10 = 302.5\pi \text{ cm}^3
$$
✔ Volume = $ 302.5\pi $ cm³
---
8)
- Diameter = 12 in → Radius $ r = 6 $ in
- Height = 13 in
$$
V = \pi (6)^2 (13) = \pi \cdot 36 \cdot 13 = 468\pi \text{ in}^3
$$
✔ Volume = $ 468\pi $ in³
---
9)
- Diameter = 7 m → Radius $ r = 3.5 $ m
- Height = 5 m
$$
V = \pi (3.5)^2 (5) = \pi \cdot 12.25 \cdot 5 = 61.25\pi \text{ m}^3
$$
✔ Volume = $ 61.25\pi $ m³
---
10) The cross-section of a pipe has a width of 6 cm and height of 15 cm. Calculate the volume.
> Note: "Width" here refers to the
diameter of the circular cross-section, and "height" is the
length of the pipe.
So:
- Diameter = 6 cm → Radius $ r = 3 $ cm
- Length (height) = 15 cm
$$
V = \pi (3)^2 (15) = \pi \cdot 9 \cdot 15 = 135\pi \text{ cm}^3
$$
✔ Volume = $ 135\pi $ cm³
---
✔ Final Answers:
| Problem | Volume |
|--------|--------|
| 1) | $ 108\pi $ m³ |
| 2) | $ 240\pi $ ft³ |
| 3) | $ 150\pi $ cm³ |
| 4) | $ 45\pi $ m³ |
| 5) | $ 147\pi $ ft³ |
| 6) | $ 128\pi $ mm³ |
| 7) | $ 302.5\pi $ cm³ |
| 8) | $ 468\pi $ in³ |
| 9) | $ 61.25\pi $ m³ |
| 10) | $ 135\pi $ cm³ |
> These are
exact volumes in terms of $ \pi $. If you need decimal approximations, just multiply by $ \pi \approx 3.14 $.
Let me know if you'd like decimal versions!
Parent Tip: Review the logic above to help your child master the concept of volume cylinder worksheets.
