If the volume of a sphere is increased by 95 5/16% without changing the shape, what will be the percentage increase in the surface area?
First we observe that, for similar figures. If a similar figure is increased by a scale factor
We require an increase of
Remember this will give us
Now this is volume, so:
We require the scale factor for area.So:
If we now subtract 1 form this, we will get the increase in area percentage: