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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: $100\%$


Team Careers360 4th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

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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