Question

Find the height of a cylinder with a surface area of 108 pi square meters. The radius of the cylinder is twice the height.

Answer 1

let
x---------> radius of the cylinder
y---------> the height of the cylinder

we know that
x=2y
[surface area of cylinder]=2*[pi*r²]+2*pi*r*h
surface area=108*pi m²
r=x
h=y
x=2y
108*pi=2*[pi*(2y)²]+2*pi*(2y)*y
108*pi=8*pi*y²+4*pi*y²
108*pi=12*pi*y²
y²=108/12
y²=9----------> y=√9--------> y=3 m
x=2y-------> x=2*3-----> x=6 m

the answer is
the height of the cylinder is 3 m