Work out the ratio between the surface area of sphere of radius 6cm and the total surface area of a hemisphere of radius 9cm.

Here you need to use two formulae; one for the surface area of a sphere (4πr²) and one for the area of a circle (πr²).

First the surface area of the 6cm radius sphere:
Area=4π(6²)=144π

Second the area of the 9cm radius hemisphere:
Area=4π(9)²/2+π(9²)=162π+81π=243π
The surface area must be divided by 2 for the hemisphere, as it is half a sphere. The area of the circular base of the hemisphere must be added, hence the πr² term.

This gives a ratio of 144π:243π. This can be simplified to 16:27 when both sides are divided by 9π.