Question

What will happen to the curved surface area of a cylinder if its radius is increased to twice the original value and height is reduced to half of the original value?

• A. It will be twice the original curved surface area.
• B. It will be half of the original curved surface area.
• C. It will be four times the original curved surface area.
• D. It will be same as the original curved surface area.

Answer 1

The correct option is D

It will be same as the original curved surface area.

Let the original curved surface area, radius and height be $S$, $r$ and $h$, respectively.

So, $S=2\pi rh$

Let the new curved surface area, radius and height be $S^{\prime }$, $r^{\prime }$ and $h^{\prime }$, respectively.

$r^{\prime }=2r$

$h^{\prime }=\frac{h}{2}$

$S^{\prime }=2\pi r^{\prime }{h}^{\prime }=2\pi \left(2r\right)\frac{h}{2}=2\pi rh$

So, $S^{\prime }=S$.