Measures and solids · Ages 14–15

Volume of a pyramid 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.A pyramid has a base area of 88 cm² and a height of 12 cm. What is its volume, in cm³?
Answer:
2.The pyramid in the picture stands on a 11 cm × 8 cm rectangle and is 9 cm high. What is its volume, in cm³?
Answer:
3.The pyramid in the picture stands on a 3 cm × 15 cm rectangle and is 12 cm high. What is its volume, in cm³?
Answer:
4.A pyramid has a base area of 70 cm² and a height of 18 cm. What is its volume, in cm³?
Answer:
5.The pyramid in the picture stands on a square of side 12 cm and has a volume of 480 cm³. How high is it, in cm?
Answer:
6.A triangular pyramid stands on a triangle 12 cm across and 5 cm high, and the pyramid is 20 cm high. What is its volume, in cm³?
Answer:
7.A triangular pyramid stands on a triangle 4 cm across and 10 cm high, and the pyramid is 18 cm high. What is its volume, in cm³?
Answer:
8.A cube of side 8 cm is split, by joining its centre to its eight corners, into 6 identical pyramids, each standing on one face of the cube. What is each pyramid's volume, in cm³?
Answer in simplest form
Answer:
9.The pyramid in the picture stands on a square of side 80 cm, and each side face's slant height (from the top to the middle of a base edge) is 58 cm. What is its volume, in cm³?
Answer:

10.The pyramid in the picture stands on a square of side 6 cm and is 9 cm high. What is its volume?
- A. 108 cm³
- B. 324 cm³
- C. 162 cm³
- D. 72 cm³
Choose the right answer
Answer:
11.The pyramid in the picture stands on a square of side 12 cm and is 6 cm high. What is its volume?
- A. 432 cm³
- B. 96 cm³
- C. 864 cm³
- D. 288 cm³
Choose the right answer
Answer:
12.A pyramid on a 4 cm × 12 cm rectangle, 15 cm high, has a volume of 240 cm³.
True or false?
Answer:

13.A chocolate is a pyramid on a square of side 8 cm, its volume 384 cm³. Find its height: put the steps in order.
- A. 13 × 64 × height = 384, so 64 × height = 1152
- B. Height = 1152 ÷ 64 = 18 cm
- C. Base area = 8 × 8 = 64
Write the letters in the right order
Working:
Answer:
14.A glass paperweight is a triangular pyramid: its base a right-angled triangle with shorter sides 4 cm and 6 cm, its height 7 cm. Each 1 cm³ of glass weighs 3 g. How many grams does it weigh?
Working:
Answer:
15.A glass pyramid stands on a square of side 33 m and is 15 m high. Its base is m², and the space inside it m³.
Fill in each blank
Working:
Answer:
16.A tent is a pyramid on a square: each side of the base 24 m, each side face's slant height 13 m. The tent is m high, and the space inside m³.
Fill in each blank
Working:
Answer:
17.A chocolate is a pyramid on a square of side 3 cm, its volume 51 cm³. Find its height: put the steps in order.
- A. Height = 153 ÷ 9 = 17 cm
- B. Base area = 3 × 3 = 9
- C. 13 × 9 × height = 51, so 9 × height = 153
Write the letters in the right order
Working:
Answer:
18.A tent is a pyramid on a square: each side of the base 6 m, each side face's slant height 5 m. The tent is m high, and the space inside m³.
Fill in each blank
Working:
Answer:

Show the answers and working

Volume of a pyramid worksheet: Answers and working

1. 352 cm³
13 × base area × height = 13 × 88 × 12 = 352 cm³.
2. 264 cm³
Base 11 × 8 = 88 cm², volume = 13 × 88 × 9 = 264 cm³.
3. 180 cm³
Base 3 × 15 = 45 cm², volume = 13 × 45 × 12 = 180 cm³.
4. 420 cm³
13 × base area × height = 13 × 70 × 18 = 420 cm³.
5. 10 cm
480 = 13 × 144 × height, so height = 3 × 480 ÷ 144 = 10 cm.
6. 200 cm³
The base is 12 × 5 ÷ 2 = 30 cm², the volume 13 × 30 × 20 = 200 cm³.
7. 120 cm³
The base is 4 × 10 ÷ 2 = 20 cm², the volume 13 × 20 × 18 = 120 cm³.
8. 2563 cm³
The cube 512 ÷ 6 = 2563 cm³; or base 8², height 4 (centre to face): 13 × 8² × 4 = 2563.
9. 89600 cm³
The top, the base's centre and an edge's middle make a right-angled triangle: height = 58² − 40² = 42 cm. Volume 13 × 80² × 42 = 89600 cm³.

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

13. C → A → B
Height = 3 × volume ÷ base = 3 × 384 ÷ 64 = 18 cm.
14. 84 g
Volume 13 × (4 × 6 ÷ 2) × 7 = 28 cm³; it weighs 28 × 3 = 84 g.
15. 1089, 5445
33 × 33 = 1089; 13 × 1089 × 15 = 5445.
16. 5, 960
The height, half the base 12 and the slant make a right-angled triangle: 13² − 12² = 5; 13 × 24² × 5 = 960.
17. B → C → A
Height = 3 × volume ÷ base = 3 × 51 ÷ 9 = 17 cm.
18. 4, 48
The height, half the base 3 and the slant make a right-angled triangle: 5² − 3² = 4; 13 × 6² × 4 = 48.

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