Question

If the surface area of a cylinder is S = 432π in2 and its diameter is 24 in, find its volume.

Answer 1

The volume of cylinder is
`864 \pi in^3`

Explanation:

Surface area of cylinder =
`2 \pi r(h+r)`

Diameter of cylinder = 24 inches

Radius of cylinder =
`(24)/(2)=12 inches`

Surface area of cylinder =
`2 \pi 12(h+12)`

We are given that the surface area of a cylinder is S = 432π sq.in.

So,
`2 \pi 12(h+12)=432 \pi`

`2 * 12(h+12) = 432\\h+12=(432)/(2 * 12)\\h=(432)/(2 * 12)-12\\h=6`

So, height = 6 inches

Volume of cylinder =
`\pi r^2 h = \pi (12)^2 * 6 =864 \pi in^3`

Hence The volume of cylinder is
`864 \pi in^3`