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

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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.

Liam P. A Level Biology tutor, GCSE Biology tutor, GCSE Maths tutor

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