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A right circular cylinder has a surface area of 96π in2 and a radius of 4 in. What is the height of the cylinder?

A8 in.
B6 in.
C16 in.
D24 in.

Verified Answer :

LammettHash

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

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

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