Question

Question 35

The curved surface area of a cylinder is reduced by ___ percent if the height is half of the original height.

Answer 1

$50\%$
The curved surface area of a cylinder with radius r and height h $=2\pi rh$
If the height is halved, the new height is $\frac{h}{2}$
Therefore , the new curved surface area of cylinder
$=2\pi r\frac{h}{2}=\pi rh$

$\therefore$ Percentage reduction in curved surface area

$=\frac{Decrease}{Original}\times 100$

$=\frac{2\pi rh-\pi rh}{2\pi rh}\times 100$

$=\frac{\pi rh}{2\pi rh}\times 100$

$=\frac{1}{2}\times 100$

$=50\%$