To solve
Question 1, we need to calculate the
volume of each cylinder using the formula:
$$
\text{Volume} = \pi r^2 h
$$
Where:
- $ r $ is the
radius of the base,
- $ h $ is the
height (or length) of the cylinder,
- $ \pi \approx 3.142 $ (we'll use this value for accuracy).
We’ll go through each part step by step.
---
(a)
- Diameter = 4 cm → Radius $ r = \frac{4}{2} = 2 $ cm
- Height $ h = 10 $ cm
$$
V = \pi r^2 h = 3.142 \times (2)^2 \times 10 = 3.142 \times 4 \times 10 = 125.68 \, \text{cm}^3
$$
Rounded to
one decimal place:
$$
\boxed{125.7} \, \text{cm}^3
$$
---
(b)
- Diameter = 8 cm → Radius $ r = \frac{8}{2} = 4 $ cm
- Height $ h = 30 $ cm
$$
V = \pi r^2 h = 3.142 \times (4)^2 \times 30 = 3.142 \times 16 \times 30 = 1507.68 \, \text{cm}^3
$$
Rounded to one decimal place:
$$
\boxed{1507.7} \, \text{cm}^3
$$
---
(c)
- Diameter = 10 cm → Radius $ r = \frac{10}{2} = 5 $ cm
- Height $ h = 9 $ cm
$$
V = \pi r^2 h = 3.142 \times (5)^2 \times 9 = 3.142 \times 25 \times 9 = 706.95 \, \text{cm}^3
$$
Rounded to one decimal place:
$$
\boxed{707.0} \, \text{cm}^3
$$
---
(d)
- Diameter = 8 mm → Radius $ r = \frac{8}{2} = 4 $ mm
- Height $ h = 2.5 $ mm
Note: Units are in
mm, so answer will be in
mm³
$$
V = \pi r^2 h = 3.142 \times (4)^2 \times 2.5 = 3.142 \times 16 \times 2.5 = 125.68 \, \text{mm}^3
$$
Rounded to one decimal place:
$$
\boxed{125.7} \, \text{mm}^3
$$
---
(e)
- Diameter = 40 cm → Radius $ r = \frac{40}{2} = 20 $ cm
- Height $ h = 25 $ cm
$$
V = \pi r^2 h = 3.142 \times (20)^2 \times 25 = 3.142 \times 400 \times 25 = 31,420 \, \text{cm}^3
$$
Rounded to one decimal place:
$$
\boxed{31,420.0} \, \text{cm}^3
$$
---
(f)
- Diameter = 5 cm → Radius $ r = \frac{5}{2} = 2.5 $ cm
- Height $ h = 17 $ cm
$$
V = \pi r^2 h = 3.142 \times (2.5)^2 \times 17 = 3.142 \times 6.25 \times 17
$$
First: $ 3.142 \times 6.25 = 19.6375 $
Then: $ 19.6375 \times 17 = 333.8375 $
Rounded to one decimal place:
$$
\boxed{333.8} \, \text{cm}^3
$$
---
✔ Final Answers:
| Part | Volume (to 1 d.p.) |
|------|---------------------|
| (a) | 125.7 cm³ |
| (b) | 1507.7 cm³ |
| (c) | 707.0 cm³ |
| (d) | 125.7 mm³ |
| (e) | 31,420.0 cm³ |
| (f) | 333.8 cm³ |
Let me know if you'd like a visual explanation or help with units!
Parent Tip: Review the logic above to help your child master the concept of volume of cylinder worksheet.
