Six practice problems asking students to calculate the volume of cylinders given various radii, diameters, and heights.

To find the volume of a cylinder, we use the formula:

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

Where:
- $ V $ is the volume,
- $ r $ is the radius of the base,
- $ h $ is the height (or length) of the cylinder,
- $ \pi \approx 3.142 $ (we'll use this value for calculations).

We will calculate the volume for each cylinder and round to one decimal place.

---

(a)

- Diameter = 4 cm → Radius $ r = \frac{4}{2} = 2 $ cm
- Height $ h = 10 $ cm

$$
V = \pi r^2 h = 3.142 \times (2)^2 \times 10 = 3.142 \times 4 \times 10 = 125.68 \, \text{cm}^3
$$

→ 125.7 cm³ (to one decimal place)

---

(b)

- Diameter = 8 cm → Radius $ r = \frac{8}{2} = 4 $ cm
- Height $ h = 30 $ cm

$$
V = 3.142 \times (4)^2 \times 30 = 3.142 \times 16 \times 30 = 1507.68 \, \text{cm}^3
$$

→ 1507.7 cm³

---

(c)

- Diameter = 10 cm → Radius $ r = \frac{10}{2} = 5 $ cm
- Height $ h = 9 $ cm

$$
V = 3.142 \times (5)^2 \times 9 = 3.142 \times 25 \times 9 = 706.95 \, \text{cm}^3
$$

→ 707.0 cm³

---

(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.

$$
V = 3.142 \times (4)^2 \times 2.5 = 3.142 \times 16 \times 2.5 = 125.68 \, \text{mm}^3
$$

→ 125.7 mm³

---

(e)

- Diameter = 40 cm → Radius $ r = \frac{40}{2} = 20 $ cm
- Length (height) $ h = 25 $ cm

$$
V = 3.142 \times (20)^2 \times 25 = 3.142 \times 400 \times 25 = 31420 \, \text{cm}^3
$$

→ 31420.0 cm³

---

(f)

- Diameter = 5 cm → Radius $ r = \frac{5}{2} = 2.5 $ cm
- Height $ h = 17 $ cm

$$
V = 3.142 \times (2.5)^2 \times 17 = 3.142 \times 6.25 \times 17 = 333.5375 \, \text{cm}^3
$$

→ 333.5 cm³

---

✔ Final Answers (to one decimal place):

| Cylinder | Volume |
|---------|--------|
| (a) | 125.7 cm³ |
| (b) | 1507.7 cm³ |
| (c) | 707.0 cm³ |
| (d) | 125.7 mm³ |
| (e) | 31420.0 cm³ |
| (f) | 333.5 cm³ |

Let me know if you'd like these converted to other units!