Volume of a Hemisphere Worksheets - Free Printable

Let’s solve each problem step by step.

We are finding the volume of a hemisphere.
The formula for the volume of a full sphere is:
> V = (4/3) × π × r³

Since a hemisphere is half of a sphere, we use:
> V = (2/3) × π × r³

We’re told to use π = 3.14, and round answers to two decimal places.

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Problem 1: Radius = 7 in

V = (2/3) × 3.14 × 7³
7³ = 343
V = (2/3) × 3.14 × 343
First: 3.14 × 343 = 1077.02
Then: (2/3) × 1077.02 = 718.013... → 718.01 in³

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Problem 2: Radius = 6 ft

V = (2/3) × 3.14 × 6³
6³ = 216
V = (2/3) × 3.14 × 216
3.14 × 216 = 678.24
(2/3) × 678.24 = 452.16 → 452.16 ft³

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Problem 3: Radius = 14 yd

V = (2/3) × 3.14 × 14³
14³ = 2744
3.14 × 2744 = 8616.16
(2/3) × 8616.16 = 5744.106... → 5744.11 yd³

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Problem 4: Diameter = 23 yd → Radius = 11.5 yd

V = (2/3) × 3.14 × (11.5)³
11.5³ = 11.5 × 11.5 × 11.5 = 132.25 × 11.5 = 1520.875
3.14 × 1520.875 = 4775.5475
(2/3) × 4775.5475 = 3183.698... → 3183.70 yd³

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Problem 5: Radius = 7.2 ft

V = (2/3) × 3.14 × (7.2)³
7.2³ = 7.2 × 7.2 × 7.2 = 51.84 × 7.2 = 373.248
3.14 × 373.248 = 1171.99872
(2/3) × 1171.99872 = 781.33248 → 781.33 ft³

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Problem 6: Diameter = 12 ft → Radius = 6 ft

This is same as Problem 2!
V = (2/3) × 3.14 × 6³ = 452.16 → 452.16 ft³

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Problem 7: Radius = 8 ft

V = (2/3) × 3.14 × 8³
8³ = 512
3.14 × 512 = 1607.68
(2/3) × 1607.68 = 1071.786... → 1071.79 ft³

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Problem 8: Diameter = 24 yd → Radius = 12 yd

V = (2/3) × 3.14 × 12³
12³ = 1728
3.14 × 1728 = 5425.92
(2/3) × 5425.92 = 3617.28 → 3617.28 yd³

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Problem 9: Diameter = 12 m → Radius = 6 m

Same radius as Problems 2 and 6 → V = 452.16 → 452.16 m³

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Final Answer:
1) 718.01 in³
2) 452.16 ft³
3) 5744.11 yd³
4) 3183.70 yd³
5) 781.33 ft³
6) 452.16 ft³
7) 1071.79 ft³
8) 3617.28 yd³
9) 452.16 m³