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A right circular cylinder has a surface area of 96π in^2 and a radius of 4 in.
What is the height of the cylinder?
A) 8 in.
B) 6 in.
C) 16 in.
D) 24 in.

Respuesta :

nobillionaireNobley
The total surface area of a crlinder is given by

[tex]TSA=2\pi rh+2\pi r^2[/tex]

Given that the area of the cylinder is [tex]96\pi\, in^2[/tex] and the radius is 4 in, then

[tex]96\pi=2\pi(4)h+2\pi(4)^2 \\ \\ =8\pi h+32\pi \\ \\ \Rightarrow96=8h+32 \\ \\ \Rightarrow8h=96-32=64 \\ \\ \Rightarrow h= \frac{64}{8} =8\, in[/tex]

Therefore, the height of the cylinder is 8 in.

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