Question

The curved surface area of a cylinder is 2π(y² – 7y + 12) and its radius is (y – 3). Find the height of the cylinder (C.S.A. of cylinder = 2πrh).

Answer 1

Let the height of cylinder be h.

Given, the curved surface area of a cylinder = 2π(y² – 7y + 12)

And radius of cylinder = y – 3

We know that,

Curved surface area of cylinder = 2πrh

∴ 2πrh = 2π(y² – 7y + 12)

⇒  2πrh = 2π(y² – 4y – 3y + 12)

= 2π[y(y – 4) – 3(y – 4)]

= 2π(y – 3)(y – 4)

⇒ 2πh = 2πr(y – 4)  ...[∵ r = (y – 3), given)]

On comparing the both sides, we get h = y – 4

Hence, the height of the cylinder is y – 4.