Question

The radius of a cylinder is doubled and its height is halved. Find the ratios of their surface areas.

Answer 1

Answer: 1:1

Step-by-step explanation:

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

Formula: Curved surface area of cylinder = $2\pi rh$

Now, if  radius of a cylinder is doubled and its height is halved, then new radius will be R= 2r and new height  will be  $H=\dfrac{1}{2}$

Now, new surface area = $2\pi RH= 2\pi(2r)\dfrac{h}{2}= 2\pi rh$

Ratio of curved surface areas : $\dfrac{\text{Surface area}}{\text{New surface area}}=\dfrac{2\pi rh}{2\pi rh}=\dfrac{1}{1}$

Hence, the ratios of their surface areas = 1:1 .