Volume calculation practice for cones, cylinders, and spheres.

Sure! Let’s solve each problem step by step. We’ll use the standard volume formulas for cones, cylinders, and spheres:

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🔷 Formulas:

- Cone:
\[
V = \frac{1}{3} \pi r^2 h
\]
- Cylinder:
\[
V = \pi r^2 h
\]
- Sphere:
\[
V = \frac{4}{3} \pi r^3
\]

We’ll compute each using \( \pi \approx 3.14 \) unless otherwise specified (some problems may expect exact answers with π, but since it’s a practice worksheet, we’ll use 3.14 for decimal answers).

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## ✔ Problem-by-Problem Solutions:

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1. Cone: r = 21 ft, h = 35 ft

\[
V = \frac{1}{3} \pi (21)^2 (35) = \frac{1}{3} \pi (441)(35) = \frac{1}{3} \pi (15435) = 5145\pi
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 5145 \times 3.14 = \boxed{16157.3} \text{ ft}^3
\]

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2. Sphere: r = 6 in

\[
V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) = 288\pi
\]
\[
V \approx 288 \times 3.14 = \boxed{904.32} \text{ in}^3
\]

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3. Cylinder: r = 4 cm, h = 15 cm

\[
V = \pi (4)^2 (15) = \pi (16)(15) = 240\pi
\]
\[
V \approx 240 \times 3.14 = \boxed{753.6} \text{ cm}^3
\]

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4. Cylinder: r = 19 m, h = 9 m

\[
V = \pi (19)^2 (9) = \pi (361)(9) = 3249\pi
\]
\[
V \approx 3249 \times 3.14 = \boxed{10205.86} \text{ m}^3
\]

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5. Cone: r = 24 in, h = 50 in

\[
V = \frac{1}{3} \pi (24)^2 (50) = \frac{1}{3} \pi (576)(50) = \frac{1}{3} \pi (28800) = 9600\pi
\]
\[
V \approx 9600 \times 3.14 = \boxed{30144} \text{ in}^3
\]

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6. Sphere: r = 3 mm

\[
V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36\pi
\]
\[
V \approx 36 \times 3.14 = \boxed{113.04} \text{ mm}^3
\]

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7. Sphere: r = 12 cm

\[
V = \frac{4}{3} \pi (12)^3 = \frac{4}{3} \pi (1728) = 2304\pi
\]
\[
V \approx 2304 \times 3.14 = \boxed{7234.56} \text{ cm}^3
\]

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8. Cylinder: r = 8 ft, h = 6 ft

\[
V = \pi (8)^2 (6) = \pi (64)(6) = 384\pi
\]
\[
V \approx 384 \times 3.14 = \boxed{1205.76} \text{ ft}^3
\]

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9. Cone: r = 3 cm, h = 6 cm

\[
V = \frac{1}{3} \pi (3)^2 (6) = \frac{1}{3} \pi (9)(6) = \frac{1}{3} \pi (54) = 18\pi
\]
\[
V \approx 18 \times 3.14 = \boxed{56.52} \text{ cm}^3
\]

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10. Cone: d = 30 m → r = 15 m, h = 29 m

\[
V = \frac{1}{3} \pi (15)^2 (29) = \frac{1}{3} \pi (225)(29) = \frac{1}{3} \pi (6525) = 2175\pi
\]
\[
V \approx 2175 \times 3.14 = \boxed{6831.5} \text{ m}^3
\]

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11. Cylinder: d = 20 cm → r = 10 cm, h = 10 cm

\[
V = \pi (10)^2 (10) = \pi (100)(10) = 1000\pi
\]
\[
V \approx 1000 \times 3.14 = \boxed{3140} \text{ cm}^3
\]

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12. Sphere: d = 20 cm → r = 10 cm

\[
V = \frac{4}{3} \pi (10)^3 = \frac{4}{3} \pi (1000) = \frac{4000}{3}\pi \approx 1333.33\pi
\]
\[
V \approx 1333.33 \times 3.14 = \boxed{4186.67} \text{ cm}^3
\]

*(Note: More precisely, \( \frac{4000}{3} \times 3.14 = 4186.666... \))*

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## 📝 Final Answers Summary:

| # | Shape | Volume (rounded to 2 decimals) |
|---|----------|-------------------------------|
| 1 | Cone | 16157.30 ft³ |
| 2 | Sphere | 904.32 in³ |
| 3 | Cylinder | 753.60 cm³ |
| 4 | Cylinder | 10205.86 m³ |
| 5 | Cone | 30144.00 in³ |
| 6 | Sphere | 113.04 mm³ |
| 7 | Sphere | 7234.56 cm³ |
| 8 | Cylinder | 1205.76 ft³ |
| 9 | Cone | 56.52 cm³ |
|10 | Cone | 6831.50 m³ |
|11 | Cylinder | 3140.00 cm³ |
|12 | Sphere | 4186.67 cm³ |

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✔ All volumes calculated using standard formulas and π ≈ 3.14.

Let me know if you’d like the answers in terms of π instead of decimals — or if you want to see step-by-step work for any specific one!