Discussion
If the radius of a sphere is increased by 50%, find the increase per cent in its surface area.
Answer: D
Surface area varies as the square of the radius.
\[ \frac{S'}{S} = \left(\frac{1.5r}{r}\right)^{2} = 2.25 \]
\[ \text{increase} = 2.25 - 1 = 1.25 = 125\% \]
The volume, which varies as the cube, would rise by \( 1.5^{3} - 1 = 2.375 \), or 237.5% - a much larger jump for the same change in radius.
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