Surface area of 3D shapes: Nets, formulae
In a nutshell
The surface area of a shape is the sum of the areas of its faces. The surface area of 3D shapes can either be calculated using nets or using given formulae.
Surface area using nets
Net
A net is a 3D shape that has been unfolded and laid out flat. Here are some examples of nets.
Surface area
To find the surface area of a shape using nets, sketch the net and work out the area of the net. This can be done by working out the area of each individual shape in the net.
Example 1
What is the surface area of a cube with side lengths 8cm?
First, sketch the net:
The net of a cube is six squares. In this example, each square will have side lengths 8cm.
Then, find the area of the net:
The net is a compound shape consisting of six squares.
The area of one of these squares is given to be:
8×8=64cm2
The area of the net is therefore:
6×64=384cm2
The surface area of the cube is 384 cm2.
Surface area formulae
These are the formulae you need to know:
SHAPE | FORMULA | DIAGRAM |
Sphere | S.A=4πr2 | |
Cylinder | S.A=2πr2+2πrh | |
Cone | Curved surface area=πrl S.A=πrl+πr2 | |
Example 2
What is the surface area of a sphere with radius 2m to three significant figures?
Substitute r=2 into the formula:
S.A=4πr2=4π(2)2=16π=50.26548246...m2
The surface area is 50.3m2 (3 s.f.).