Question

Radius of base of right circular cylinder is increased by 75% and height decreased by 50% ,find increase or decrease in curved surface area

Answer 1

★ SURFACE AREA AND VOLUME ★

Let the radius and height of the cylinder be r and h.

So,Curved surface area of cylinder $= 2 \pi rh$

Here, Given radius increased by 75%, hence new radius $= r+ \frac{3r}{4} = \frac{7}{4}$

⇒ Height is decreased by 50%, hence new height $= h- \frac{h}{2} = \frac{h}{2}$

Now, Curved surface area of new cylinder $= 2 \pi (\frac{7r}{4}) (\frac{h}{2}) = \frac{7}{4} \pi rh$

⇒ Decrease in curved surface area = $2 \pi rh - \frac{7}{4} \pi rh= \pi rh$

∴ Percent decrease  $= \frac{ \pi rh}{2\pi rh}$ × $100$ 

                                   $= 50%$