Question : If the radius of a cylinder is increased by 25%, by how much percentage the height must be reduced, so that the volume of the cylinder remains the same.
Option 1: 36
Option 2: 56
Option 3: 64
Option 4: 46
Correct Answer: 36
Solution :
Given: The radius of a cylinder is increased by 25%.
Volume of the cylinder = $\pi r^2 h$
Let $h$ be the initial height, $r$ be the initial radius, $H$ be the final height and the new radius will be $\frac{125}{100}r$ = $\frac{5}{4}r$.
According to the question,
$\pi\times r^2\times h=\pi\times(\frac{5}{4}r)^2\times H$
$⇒h=\frac{25}{16}\times H$
$⇒\frac{h}{H}=\frac{25}{16}$
The decrease in percentage in the height is $\frac{(h-H)}{h}\times 100$
= $\frac{(25-16)}{25}\times 100$
= 9 × 4 = 36%
Hence, the correct answer is 36.
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