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CFreitas · Answer 1 · 2018-04-29T01:22:42+0000

The surface area of a right cylinder is the sum of the areas of the lateral face and the circular bases. The lateral face is really just a rectangle with the same height as the cylinder and a length equal to the circumference of the circular base.

If the radius of the base is

and the height is

, then the surface area of the cylinder is

$A=2\pi r^2+2\pi rh$

You're given that the area is
$96\pi$ and the radius is

, so you have

$96\pi=2\pi*4^2+2\pi*4h\implies 12=4+h\implies h=8$

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