Worksheet for calculating the volume of spheres using the formula V = 4/3πr³, with given radii and diameters.

We are given the formula for the volume of a sphere:
V = (4/3)πr³
where r is the radius.

⚠️ Important note: For some spheres, the image shows the diameter, not the radius.
→ So we must remember: radius = diameter ÷ 2

Let’s solve each one step by step.

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🟡 Sphere 1: Radius = 5 in.

- r = 5
- V = (4/3) × π × 5³
- 5³ = 125
- V = (4/3) × π × 125 = (500/3)π ≈ 166.666...π
→ V = 166.7π in³ (to one decimal place)

✔ Final Answer:
V = 166.7π in³

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🟢 Sphere 2: Radius = 7 ft

- r = 7
- V = (4/3) × π × 7³
- 7³ = 343
- V = (4/3) × π × 343 = (1372/3)π ≈ 457.333...π
→ V = 457.3π ft³

✔ Final Answer:
V = 457.3π ft³

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🟣 Sphere 3: Radius = 3 cm

- r = 3
- V = (4/3) × π × 3³
- 3³ = 27
- V = (4/3) × π × 27 = (108/3)π = 36π
→ V = 36.0π cm³

✔ Final Answer:
V = 36.0π cm³

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🟠 Sphere 4: Diameter = 12 yd → Radius = 6 yd

- r = 12 ÷ 2 = 6
- V = (4/3) × π × 6³
- 6³ = 216
- V = (4/3) × π × 216 = (864/3)π = 288π
→ V = 288.0π yd³

✔ Final Answer:
V = 288.0π yd³

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🔵 Sphere 5: Diameter = 18 mm → Radius = 9 mm

- r = 18 ÷ 2 = 9
- V = (4/3) × π × 9³
- 9³ = 729
- V = (4/3) × π × 729 = (2916/3)π = 972π
→ V = 972.0π mm³

✔ Final Answer:
V = 972.0π mm³

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🔴 Sphere 6: Diameter = 28 m → Radius = 14 m

- r = 28 ÷ 2 = 14
- V = (4/3) × π × 14³
- 14³ = 14 × 14 × 14 = 196 × 14 = 2744
- V = (4/3) × π × 2744 = (10976/3)π ≈ 3658.666...π
→ V = 3658.7π m³

✔ Final Answer:
V = 3658.7π m³

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## ✔ FINAL ANSWERS:

| Sphere | Radius/Diameter | Volume (to one decimal place) |
|--------|------------------|-------------------------------|
| 1 | 5 in | 166.7π in³ |
| 2 | 7 ft | 457.3π ft³ |
| 3 | 3 cm | 36.0π cm³ |
| 4 | 12 yd (diam) | 288.0π yd³ |
| 5 | 18 mm (diam) | 972.0π mm³ |
| 6 | 28 m (diam) | 3658.7π m³ |

All answers are expressed as multiples of π, as requested. If you need numerical values (using π ≈ 3.1416), let me know — but the problem says to leave answers in terms of π.