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Ignition Learning — Activity Sheet

Volume of prisms

Mathematics · Year 7

Name: ______________________Date: ____________

Volume measures how much space a 3D object takes up, measured in cubic units like cm³ or m³. For a rectangular prism, volume = length × width × height. For any right prism (a 3D shape with a constant cross-section, like a triangular prism), the volume is the area of the cross-section (the flat end shape) multiplied by the length of the prism. Volume is always found by multiplying an area (2D) by a length (1D), giving a 3D measurement.

Example

A rectangular box 4cm long, 3cm wide and 2cm high has volume = 4 × 3 × 2 = 24cm³. A triangular prism with a triangular cross-section area of 6cm² and a length of 10cm has volume = 6 × 10 = 60cm³.

Key terms

Volume:: The amount of space a 3D object takes up, in cubic units.
Cross-section:: The flat shape you'd see if you sliced straight through a prism.
Right prism:: A 3D shape with a constant cross-section along its length.

Questions

1. Volume measures:
- Distance
- How much space an object takes up
- Weight
- Time
2. Volume is measured in:
- cm
- cm²
- cm³
- kg
3. The formula for the volume of a rectangular prism is:
- l × w
- l + w + h
- l × w × h
- 2l + 2w
4. A cross-section is:
- The whole 3D shape
- The flat shape seen when you slice through it
- The colour of a shape
- The perimeter
5. A rectangular prism 2cm × 3cm × 4cm has a volume of:
- 9cm³
- 12cm³
- 24cm³
- 48cm³
6. For a right prism, volume =
- Area of cross-section + length
- Area of cross-section × length
- Perimeter × length
- Area × 2
7. A cube with side length 3cm has a volume of:
- 9cm³
- 18cm³
- 27cm³
- 81cm³
8. A box is 5cm long, 4cm wide and 2cm high. What is its volume?
- 11cm³
- 20cm³
- 40cm³
- 400cm³
9. A triangular prism has a cross-section area of 8cm² and a length of 6cm. What is its volume?
- 14cm³
- 24cm³
- 48cm³
- 480cm³
10. A cube has a side length of 5cm. What is its volume?
- 15cm³
- 25cm³
- 100cm³
- 125cm³
11. A rectangular prism has a volume of 60cm³, a length of 5cm and a width of 4cm. What is its height?
- 3cm
- 4cm
- 5cm
- 12cm
12. A fish tank is 40cm long, 20cm wide and 30cm high. What is its volume in cm³?
- 90
- 900
- 24000
- 2400
13. A triangular prism cross-section has an area of 15cm². If its volume is 150cm³, what is its length?
- 5cm
- 10cm
- 15cm
- 150cm
14. Two boxes have the same volume. Box A is 2×3×4, Box B is 6×2×2. Do they have the same volume?
- Yes
- No
- Cannot tell
- Only if identical shape
15. A rectangular prism has volume 240cm³. Its length is 8cm and height is 5cm. What is its width?
- 4cm
- 6cm
- 8cm
- 40cm
16. A swimming pool is 10m long, 5m wide and 1.5m deep. How many cubic metres of water does it hold?
- 15
- 50
- 75
- 150
17. A triangular prism has a triangular cross-section with base 6cm and height 4cm (area = 12cm²), and a length of 9cm. What is its volume?
- 54cm³
- 108cm³
- 216cm³
- 27cm³
18. Doubling the length of a rectangular prism while keeping width and height the same will:
- Halve the volume
- Double the volume
- Quadruple the volume
- Not change the volume
19. A cube's volume is 64cm³. What is its side length?
- 4cm
- 8cm
- 16cm
- 21.3cm
20. If a rectangular prism's length, width and height are all doubled, its volume becomes:
- 2 times as large
- 4 times as large
- 6 times as large
- 8 times as large

Answer key (parent copy)

1. How much space an object takes up
2. cm³
3. l × w × h
4. The flat shape seen when you slice through it
5. 24cm³
6. Area of cross-section × length
7. 27cm³
8. 40cm³
9. 48cm³
10. 125cm³
11. 3cm
12. 24000
13. 10cm
14. Yes
15. 6cm
16. 75
17. 108cm³
18. Double the volume
19. 4cm
20. 8 times as large