Question

The radius of the rate of the right circular cylinder is increased by $75\%$ and height is decreased by $50\%$ Find the percentage increase or deceases inits curved surface area.

Answer 1

Curved surface area of cylinder $\left(S_1\right)=2\pi rh$

radius is increased by $75$%

So,new radius $=1.75r$

height is decreased by $50$% so the

new heights $0.5h$

Curved surface area $\left(S_2\right)=2\pi \left(1.75\right)r\left(0.5h\right)$

$=1.75\pi rh$

Curved surface area decreases by $=\left(\frac{2\pi rh-1.75\pi rh}{2\pi rh}\times 100\right)$%

$=\left(\frac{0.25\pi rh}{2\pi rh}\times 100\right)$%

$=12.5$%