Measures and solids · Ages 14–15

Volume of a sphere worksheet

Part of: Cones & spheres

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Measures and solids · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The sphere in the picture has a radius of 18 cm. What is its volume, in terms of π?
Answer:
2.The hemisphere in the picture has a radius of 15 cm. What is its volume, in terms of π?
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3.The sphere in the picture has a radius of 15 cm. What is its volume, in terms of π?
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4.The sphere in the picture has a volume of 972π cm³. What is its radius, in cm?
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5.Taking π as 3.14, what is the volume of the sphere in the picture (radius 3 cm), in cm³?
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6.A cylinder holds a ball exactly: the ball touches its top, its bottom and its side. The cylinder's volume is 1458π cm³. What is the ball's volume, in terms of π?
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7.The hemisphere in the picture is 10 cm across. Correct to 1 decimal place, what is its volume, in cm³?
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8.A cylinder holds a ball exactly: the ball touches its top, its bottom and its side. The cylinder's volume is 3456π cm³. What is the ball's volume, in terms of π?
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9.The hemisphere in the picture is 25 cm across. Correct to 1 decimal place, what is its volume, in cm³?
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13.A ball is 36 cm across. Its volume is π cm³ in terms of π, and cm³ taking π as 3.14.
Fill in each blank
Working:
Answer:
14.A round fish bowl, a sphere, holds 36π cm³. Find its radius: put the steps in order.
- A. 43 × π × r³ = 36π
- B. r = 3 cm
- C. 4 × r³ = 108, so r³ = 27
Write the letters in the right order
Working:
Answer:
15.A hemispherical bowl has an inner radius of 11 cm. Correct to 1 decimal place, how many litres of water can it hold at most?
Working:
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16.A box holds 40 steel balls of radius 0.5 cm, and each 1 cm³ of steel weighs 7.8 g. Taking π as 3.14, how many grams do the balls weigh, to the nearest gram?
Working:
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17.A hemispherical bowl has an inner radius of 15 cm. Correct to 1 decimal place, how many litres of water can it hold at most?
Working:
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18.A round fish bowl, a sphere, holds 4500π cm³. Find its radius: put the steps in order.
- A. 43 × π × r³ = 4500π
- B. r = 15 cm
- C. 4 × r³ = 13500, so r³ = 3375
Write the letters in the right order
Working:
Answer:

Show the answers and working

Volume of a sphere worksheet: Answers and working

1. 7776 π cm³
43 × π × 18³ = 43 × 5832π = 7776π cm³.
2. 2250 π cm³
A hemisphere is half a sphere: 12 × 43 × π × 15³ = 23 × π × 15³ = 2250π cm³.
3. 4500 π cm³
43 × π × 15³ = 43 × 3375π = 4500π cm³.
4. 9 cm
43 × πr³ = 972π, so r³ = 3 × 972 ÷ 4 = 729 and r = 9 cm.
5. 113.04 cm³
43 × π × 3³ = 36π; with 3.14, 113.04 cm³.
6. 972 π cm³
Archimedes: the ball is 23 of the cylinder: 23 × 1458π = 972π cm³. (The cylinder is πr² × 2r = 2πr³, so r = 9.)
7. 261.8 cm³
Radius 10 ÷ 2; 23 × π × radius³ with the calculator's π: about 261.8 cm³.
8. 2304 π cm³
Archimedes: the ball is 23 of the cylinder: 23 × 3456π = 2304π cm³. (The cylinder is πr² × 2r = 2πr³, so r = 12.)
9. 4090.6 cm³
Radius 25 ÷ 2; 23 × π × radius³ with the calculator's π: about 4090.6 cm³.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 7776, 24416.64
Radius 18: 43 × π × 18³ = 7776π; × 3.14 = 24416.64.
14. A → C → B
Divide by π and multiply by 3: 4r³ = 108, r³ = 27, and the cube root is 3 cm.
15. 2.8 L
23 × π × 11³ cm³, and 1 L = 1000 cm³: about 2.8 L.
16. 163 g
Each is 43 × 3.14 × 0.5³; × 40 balls × 7.8 g: about 163 g.
17. 7.1 L
23 × π × 15³ cm³, and 1 L = 1000 cm³: about 7.1 L.
18. A → C → B
Divide by π and multiply by 3: 4r³ = 13500, r³ = 3375, and the cube root is 15 cm.

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