Volume · Year 9
In Year 9 you get fluent with: 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
- Any prism: V = area of cross-section × length.
- Cylinder: V = πr²h.
Worked examples
Example 1
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 2
A prism has a cross-section with an area of 15 cm² and is 8 cm long. Find its volume.
Answer: 120 cm³
Example 3
A triangular prism is 10 cm long. Its end is a triangle with base 6 cm and height 4 cm. Find its volume.
Answer: 120 cm³
Example 4
A cylinder has radius 3 cm and height 10 cm. Find its volume, to 1 d.p.
Answer: 282.7 cm³