# 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:*

*$8\times8=64cm^2$*

*The area of the net is therefore:*

$6\times64=384cm^2$

*The surface area of the cube is *$\underline{384 \ cm^2}$.

## Surface area formulae

These are the formulae you need to know:

**SHAPE** | **FORMULA** | **DIAGRAM** |

Sphere | $S.A=4\pi r^2$ | |

Cylinder | $S.A=2\pi r^2 +2\pi rh$ | |

Cone | $\text{Curved surface area}=\pi rl$ $S.A=\pi rl +\pi r^2$ | |

##### Example 2

*What is the surface area of a sphere with radius $2m$ to three significant figures?*

*Substitute $r=2$ into the formula:*

$\begin{aligned}S.A&=4\pi r^2\\&=4\pi (2)^2\\&=16\pi\\&=50.26548246...m^2\end{aligned}$

*The surface area is *$\underline{50.3m^2\space\ (3\space s.f.)}$.