Question

The radius of the base and the height of a right circular cylinder are each increased by 10%, then the volume of the cylinder is increased by

• A. 30%
• B. 40%
• C. 42%
• D. 33.1%

Answer 1

Answer: (D)

Let the original radius and height be $r$ and $h$, respectively.

So, the volume of cylinder $=\pi r^{2}h$ $.......\left(1\right)$

Since, the radius and height are each increased by $10\%$, then

The new radius $=1.1r$ and new height $=1.1h$.

Therefore, the new volume of the cylinder will be

$=\pi (1.1r{)}^2\times (1.1h)$

$=1.331\times \pi r^{2}h$ $.........\left(2\right)$

Therefore, the required percentage

$=\frac{1.331\pi r^{2}h-\pi r^{2}h}{\pi r^{2}h}\times 100$

$=\frac{0.331\pi r^{2}h}{\pi r^{2}h}\times 100$

$=33.1\%$

Hence, this is the answer.