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

Question

asked Dec 8, 2021 114k views

1 Answer

Michael Mason · Answer 1 · 2021-12-14T17:32:54+0000

Answer:

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
$864 \pi in^3$