Volume · Year 10
In Year 10 you learn: cones, pyramids and spheres.
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 prism has a cross-section with an area of 15 cm² and is 8 cm long. Find its volume.
Answer: 120 cm³
Example 2
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 3
A cylinder has radius 3 cm and height 10 cm. Find its volume, to 1 d.p.
Answer: 282.7 cm³
Example 4
A cylinder has a volume of 90π cm³ and a radius of 3 cm. Find its height.
Answer: 10 cm
Example 5
Find the volume of a sphere with radius 3 cm, to 1 decimal place.
Answer: 113.1 cm³