Volume · Year 8
In Year 8 you learn: volume of prisms and cylinders.
Volume is how much space a solid takes up, measured in cubic units such as cm³ and m³. Count the cubes, or multiply: for a cuboid, length × width × height; for any prism or cylinder, the area of the cross-section × the length.
Key facts
- Volume is measured in cubic units: count the 1 cm cubes that fill a solid.
- Cuboid: V = length × width × height.
- Any prism: V = area of cross-section × length.
- Cylinder: V = πr²h.
- 1 litre = 1,000 cm³, and 1 cm³ holds 1 ml.
Worked examples
Example 1
Find the volume of a cube with edges of 4 cm.
Answer: 64 cm³
Example 2
A cuboid is 5 cm long, 3 cm wide and 2 cm high. Find its volume.
Answer: 30 cm³
Example 3
A box is filled with 1 cm cubes: 5 along, 3 deep and 2 layers high. How many cubes fill it, and what is its volume?
Answer: 30 cubes, 30 cm³
Example 4
A fish tank is 60 cm long, 30 cm wide and 40 cm tall. A tap fills it at 6 litres per minute. How long does it take to fill?
Answer: 12 minutes
Example 5
A cuboid has a volume of 60 cm³. It is 5 cm long and 4 cm wide. How tall is it?
Answer: 3 cm
Example 6
A prism has a cross-section with an area of 15 cm² and is 8 cm long. Find its volume.
Answer: 120 cm³