Question : If the radius of a right circular cylinder open at both ends is decreased by 25% and the height of the cylinder is increased by 25%, the curved surface area of the cylinder thus formed:
Option 1: remains unaltered
Option 2: is increased by $25\%$
Option 3: is increased by $6.25\%$
Option 4: is decreased by $6.25\%$
Correct Answer: is decreased by $6.25\%$
Solution :
The curved surface area of a right circular cylinder before the change, where $r$ is the radius and $h$ is the height $ = 2\pi rh$
The radius is decreased by $25\%$,
$r' = 0.75r$
The height is increased by $25\%$,
$h' = 1.25h$
The curved surface area of a right circular cylinder after the change
$= 2\pi r' h' = 2\pi (0.75r)(1.25h) = 2\pi rh × 0.75 × 1.25 =1.875\pi rh$
$\therefore$ Percentage change = $(\frac{2\pi rh-1.875\pi rh}{2\pi rh})×100= 6.25\%$
Hence, the correct answer is 'is decreased by $6.25\%$'.
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