Question : If the base radius and the height of a right circular cone are increased by 10%, then the percentage increase in the volume is:
Option 1: 30.2%
Option 2: 22.1%
Option 3: 33.1%
Option 4: 20.2%
Correct Answer: 33.1%
Solution :
Given,
The base radius and the height of a right circular cone are increased by 10%
We know the volume of the cone = $\frac13\pi r^2h$, where r is the radius and h is the height.
Volume $\propto$ $r^2$
Volume $\propto$ $h$
Let the original volume be 100 units
⇒ Volume after 10% increase in radius and height = 100 × 110% × 110% × 110%
= $100 × \frac{110}{100}×\frac{110}{100}×\frac{110}{100}$
= 133.1
⇒ Increase percent = 33.1%
Hence, the correct answer is 33.1%.
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