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Volume of 3D Shapes

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Volume of 3D Shapes

Choose the best answer where options are given. Show your working for calculations. Use π = 3.14 unless a question says otherwise.

Understanding volume

1.Which statement best describes the volume of a solid object?

The length of its outer boundary
The amount of three-dimensional space it occupies
The total area of its outside faces
The distance from its base to its top

2.Select every unit that could be used to state a volume.

mm³
cm²
m³
L
km

3.Match each solid to its most specific formula for calculating volume.

Cube with side length s
Rectangular prism
Cylinder
Triangular prism
Prism with any uniform cross-section

V = l × w × h
V = πr²h
V = (½ × base × triangle height) × prism length
V = s³
V = cross-sectional area × prism length

Calculate volume

4.A cube has an edge length of 7 cm. Calculate its volume.

5.A rectangular prism is 9 cm long, 4 cm wide, and 6 cm high. Find its volume.

6.A cylindrical container has a radius of 3 cm and a height of 8 cm. Using π = 3.14, calculate its volume to 2 decimal places.

7.A storage crate measures 60 cm by 35 cm by 25 cm internally. What volume of space does it hold?

Apply and extend

8.A cylindrical rainwater tank has a diameter of 5 m and a height of 2.4 m. Calculate its volume in cubic metres using π = 3.14. Give your answer to 2 decimal places.

9.A moving box is 45 cm long, 30 cm wide, and 28 cm high. What is its volume in litres? Use 1,000 cm³ = 1 L.

10.A cube has side length 4 cm. A second cube has each side twice as long. How many times the volume of the first cube is the volume of the second cube? Show this using both volumes.