Surface area · Year 10
In Year 10 you learn: surface area of spheres and cones.
Surface area is the total area of all the faces of a solid, measured in square units such as cm². Unfold the solid into its net, find the area of each face, and add them up.
Key facts
- A prism's surface: two ends plus a rectangle for each side.
- Cylinder: curved surface = 2πrh; total surface = 2πr² + 2πrh.
- Sphere: surface area = 4πr².
Worked examples
Example 1
A triangular prism is 10 cm long. Its ends are right-angled triangles with sides of 3 cm, 4 cm and 5 cm. Find its surface area.
Answer: 132 cm²
Example 2
Find the curved surface area of a cylinder with radius 4 cm and height 6 cm, to 1 decimal place.
Answer: 150.8 cm²
Example 3
Find the total surface area of a cylinder with radius 2 cm and height 5 cm, to 1 decimal place.
Answer: 88.0 cm²
Example 4
Find the surface area of a sphere with radius 5 cm, to 1 decimal place.
Answer: 314.2 cm²