Question

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

Answer 1

The curved surface area of a cylinder with radius ${}^{\prime }{r}^{\prime }$ and height ${}^{\prime }{h}^{\prime }$ $=2\pi rh$
If the height is halved, the new height is $\frac{h}{2}$
Therefore , the new curved surface area of cylinder
$=2\pi r\left(\frac{h}{2}\right)=\pi rh$

$\therefore$ Percentage reduction in curved surface area

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

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

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

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

$=50\%$

Hence, the curved surface area will reduce by $50\%$ when height will become half.