Spheres

The formula for the volume of a sphere is:

Sphere with r labelled

\text{volume of a sphere} = \frac{4}{3} \pi r^3

The surface area of a sphere can be calculated using the formula:

Sphere

\text{surface area of a sphere} = 4 \pi r^2

Example

Calculate the volume and surface area of a football with a radius of 12 cm to 1 decimal place.

\begin{array}{rcl} \text{Volume} & = & \frac{4}{3} \pi r^3 \\ & = & \frac{4}{3} \times \pi \times 12^3 \\ & = & 7,238.2~\text{cm}^3 \end{array}

\begin{array}{rcl} \text{Surface area} & = & 4 \pi r^2 \\ & = & 4 \times \pi \times 12^2 \\ & = & 1,809.6~\text{cm}^2 \end{array}