Surface area · Year 9

In Year 9 you learn: surface area of prisms and cylinders.

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

  • Surface area: add the areas of all the faces (a net helps).
  • A cube has 6 equal square faces; a cuboid has 3 pairs of matching rectangles.
  • A prism's surface: two ends plus a rectangle for each side.
  • Cylinder: curved surface = 2πrh; total surface = 2πr² + 2πrh.

Worked examples

Example 1

Find the surface area of a cube with edges of 3 cm.

Answer: 54 cm²

Example 2

Find the surface area of a cuboid 5 cm by 4 cm by 2 cm.

Answer: 76 cm²

Example 3

A cuboid is 6 cm long, 5 cm deep and 4 cm tall. Find its volume and its surface area.

Answer: Volume 120 cm³, surface area 148 cm²

Example 4

A cube has a surface area of 150 cm². How long is each edge?

Answer: 5 cm

Example 5

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 6

Find the curved surface area of a cylinder with radius 4 cm and height 6 cm, to 1 decimal place.

Answer: 150.8 cm²

Other years