Question : If the area of the base of a cone is increased by 100%, the volume increases by:
Option 1: $200\%$
Option 2: $182\%$
Option 3: $141\%$
Option 4: $100\%$
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Correct Answer: $100\%$
Solution :
The volume $(V)$ of a cone,
$V = \frac{1}{3} \pi r^2 h$
The area of the base $=\pi r^2$
After $100\%$ increase in the area of the new base $=2\pi r^2$
The new volume $(V')$ of the cone,
$V' = \frac{1}{3} (2\pi r^2) h = 2V$
$\therefore$ The change in volume $=\frac{2V-V}{V}×100=100\%$
Hence, the correct answer is $100\%$.
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