Volume of a Hemisphere Worksheets - Free Printable

Let’s solve each problem one by one.

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 = 5 in

V = (2/3) × 3.14 × (5)³
= (2/3) × 3.14 × 125
= (2/3) × 392.5
= 785 / 3 ≈ 261.67 in³

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Problem 2: Diameter = 18 ft → Radius = 9 ft

V = (2/3) × 3.14 × (9)³
= (2/3) × 3.14 × 729
= (2/3) × 2289.06
= 4578.12 / 3 ≈ 1526.04 ft³

Wait — let me recalculate that multiplication:

3.14 × 729 = ?

3 × 729 = 2187
0.14 × 729 = 102.06
Total = 2187 + 102.06 = 2289.06

Then (2/3) × 2289.06 = (2 × 2289.06) ÷ 3 = 4578.12 ÷ 3 = 1526.04

✔ Correct.

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Problem 3: Radius = 14 yd

V = (2/3) × 3.14 × (14)³
14³ = 14 × 14 × 14 = 196 × 14 = 2744

So:
(2/3) × 3.14 × 2744
First: 3.14 × 2744 = ?

Let’s compute:

3 × 2744 = 8232
0.14 × 2744 = 384.16
Total = 8232 + 384.16 = 8616.16

Now multiply by 2/3:
(2 × 8616.16) ÷ 3 = 17232.32 ÷ 3 ≈ 5744.11 yd³

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

V = (2/3) × 3.14 × (11.5)³

First, 11.5³ = 11.5 × 11.5 × 11.5

11.5 × 11.5 = 132.25
132.25 × 11.5 = ?

Break it down:

132.25 × 10 = 1322.5
132.25 × 1.5 = 198.375
Total = 1322.5 + 198.375 = 1520.875

Now:
(2/3) × 3.14 × 1520.875

First: 3.14 × 1520.875

3 × 1520.875 = 4562.625
0.14 × 1520.875 = 212.9225
Total = 4562.625 + 212.9225 = 4775.5475

Now × 2/3:
(2 × 4775.5475) ÷ 3 = 9551.095 ÷ 3 ≈ 3183.70 yd³

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Problem 5: Radius = 7.2 in

V = (2/3) × 3.14 × (7.2)³

7.2³ = 7.2 × 7.2 × 7.2

7.2 × 7.2 = 51.84
51.84 × 7.2 = ?

50 × 7.2 = 360
1.84 × 7.2 = 13.248
Total = 360 + 13.248 = 373.248

Now:
(2/3) × 3.14 × 373.248

First: 3.14 × 373.248

3 × 373.248 = 1119.744
0.14 × 373.248 = 52.25472
Total = 1119.744 + 52.25472 = 1171.99872

Now × 2/3:
(2 × 1171.99872) ÷ 3 = 2343.99744 ÷ 3 ≈ 781.33 in³

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Problem 6: Diameter = 13 ft → Radius = 6.5 ft

V = (2/3) × 3.14 × (6.5)³

6.5³ = 6.5 × 6.5 × 6.5

6.5 × 6.5 = 42.25
42.25 × 6.5 = ?

40 × 6.5 = 260
2.25 × 6.5 = 14.625
Total = 260 + 14.625 = 274.625

Now:
(2/3) × 3.14 × 274.625

First: 3.14 × 274.625

3 × 274.625 = 823.875
0.14 × 274.625 = 38.4475
Total = 823.875 + 38.4475 = 862.3225

Now × 2/3:
(2 × 862.3225) ÷ 3 = 1724.645 ÷ 3 ≈ 574.88 ft³

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Problem 7: Radius = 8 ft

V = (2/3) × 3.14 × (8)³
8³ = 512

(2/3) × 3.14 × 512

First: 3.14 × 512 = ?

3 × 512 = 1536
0.14 × 512 = 71.68
Total = 1536 + 71.68 = 1607.68

Now × 2/3:
(2 × 1607.68) ÷ 3 = 3215.36 ÷ 3 ≈ 1071.79 ft³

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

V = (2/3) × 3.14 × (12)³
12³ = 1728

(2/3) × 3.14 × 1728

First: 3.14 × 1728

3 × 1728 = 5184
0.14 × 1728 = 241.92
Total = 5184 + 241.92 = 5425.92

Now × 2/3:
(2 × 5425.92) ÷ 3 = 10851.84 ÷ 3 = 3617.28 yd³

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Problem 9: Diameter = 22 m → Radius = 11 m

V = (2/3) × 3.14 × (11)³
11³ = 1331

(2/3) × 3.14 × 1331

First: 3.14 × 1331

3 × 1331 = 3993
0.14 × 1331 = 186.34
Total = 3993 + 186.34 = 4179.34

Now × 2/3:
(2 × 4179.34) ÷ 3 = 8358.68 ÷ 3 ≈ 2786.23 m³

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Final Answer:

1) 261.67 in³
2) 1526.04 ft³
3) 5744.11 yd³
4) 3183.70 yd³
5) 781.33 in³
6) 574.88 ft³
7) 1071.79 ft³
8) 3617.28 yd³
9) 2786.23 m³