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

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=(1)/(2)`

Now, new surface area =
`2\pi RH= 2\pi(2r)(h)/(2)= 2\pi rh`

Ratio of curved surface areas :
`\frac{\text{Surface area}}{\text{New surface area}}=(2\pi rh)/(2\pi rh)=(1)/(1)`

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