Discussion
Suresh wanted to keep volume of his right circular cone shaped cap same, but increase its height to 9 times. By how much should he increase or decrease the radius?
Answer: B
The volume must stay fixed while the height grows ninefold.
\[ V = \frac{1}{3}\pi r^{2} h = \frac{1}{3}\pi r'^{2}(9h) \]
\[ r^{2} = 9r'^{2} \quad\Longrightarrow\quad r' = \frac{r}{3} \]
So the radius must be reduced to one third. Because volume depends on \( r^{2} \), a ninefold change in height is offset by a change of only \( \sqrt{9} = 3 \) in the radius - reducing it to one ninth would shrink the volume to a ninth of what it should be.
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