Question : If the radius of the base, and the height of a right circular cone are increased by 20%, what is the approximate percentage increase in volume?
Option 1: 60
Option 2: 68.8
Option 3: 72.8
Option 4: 75
Correct Answer: 72.8
Solution :
Let the base radius and height of the cone be r and h respectively
Then, volume = $\frac{1}{3}\pi r^2h=V$
If base radius is increased 20 %, new radius = $r\times \frac{120}{100}=\frac{6}{5}r$
Similarly, New height = $\frac{6}{5}h$
New volume = $\frac{1}{3}(\frac{6}{5}r)^2\times \frac{6}{5}h=\frac{216}{125} V$
Hence, percentage increase = $\frac{(\frac{216}{125}-1)V}{V}\times 100=72.8\%$
Hence, the correct answer is 72.8.
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