Question

HELP ASAP THIS IS STRESSING ME OUT!

Answer 1

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 $r$ and the height is $h$, 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 $4$, so you have

$96\pi=2\pi\times4^2+2\pi\times4h\implies 12=4+h\implies h=8$