Question

The diameter of a right circular cylinder increases by $50$% and its height decreases by $40$%, then finds the percentage change in its curved surface area.

• A. $20$% decrease
• B. $10$% decrease
• C. $10$% increase
• D. $20$% increase

Answer 1

The correct option is B $10$% decrease

Given, a right circular cylinder with diameter $d$ and height $h$

Curved surface area $=2\pi rh$

$=2\pi \times \frac{d}{2}\times h$ ....(As radius is half of diameter)
$=\pi dh$

Diameter is increased by $50\%$ $=d+$ $0.5$ $d$ $=1.5$ $d$

Height is decreased by $40\%$ $=h-$ $0.4$ $h$ $=0.6$ $h$

Radius $=$ $\frac{d}{2}$ $=0.75$ $d$

New Curved surface area $=2\pi rh$

$=2\times \pi \times 0.75d\times 0.6h$

$=0.9\pi dh$

Since new curved surface area is less, so there is a decrease in curved surface area.

$\%$ decrease $=$ $\frac{C.S.A-NewC.S.A}{C.S.A}\times 100$ $\%$

$=\frac{\pi dh-0.9\pi dh}{\pi dh}\times 100$ $\%$

$=\frac{0.1\pi dh}{\pi dh}\times 100$ $\%$

$=10\%$