Question

If the radius of a cylinder is doubled and the height is halved, what is the ratio between the new curved surface area and the previous curved surface area of the cylinder?

• A. $1:1$
• B. $2:1$
• C. $3:2$
• D. $2:3$

Answer 1

The correct option is A $1:1$

Let radius of base of cylinder be 'r' and height be 'h' CSA of cylinder, $S_1=2\pi rh$

New radius $=2r$, New height $=\frac{h}{2}$

$\therefore$ New CSA, $S_2=2\pi \left(2r\right)\times \frac{h}{2}=2\pi rh$

Now, $\frac{S_1}{S_2}=\frac{2\pi rh}{2\pi rh}=1:1$