Question

The radius of cylinder A is 4 times the radius of cylinder B, and the height of cylinder A is 4 times the height of cylinder B. What is the ratio of the lateral surface area of A to the lateral surface area of B?​

Answer 1

Answer: The ratio of A's lateral surface area to B's lateral surface area is 16:1.

Step-by-step explanation: Let B's radius be x and the height be y. Then, the radius of A will be 4x and the height will be 4y.

As we know, the formula for the lateral surface area of a cylinder is

2
`\pi`rh.

So, the lateral surface area of A is 2
`\pi`(4x)(4y)= 32
`\pi`xy

lateral surface area of B is 2
`\pi`(x)(y)= 2
`\pi`xy

Ratio,

Lateral surface area of A/ Lateral surface area of B =
`(32\pi xy)/(2\pi xy)`

=
`(16)/(1)`

=16:1