Question

What is the height of cylinder with a surface area of 226.08 square meters and a radius of 3 meters? (Use 3.14 for π.)


27 meters
18 meters
3 meters
9 meters

Answer 1

Well, you know the surface area of the top(and bottom) to be:
\[\pi*r^2\]
And, the surface area of the outside part of the cylinder is
\[2*\pi*r*h\]
So, now, our total surface area is
\[2*\pi*r*h+\pi*r^2+\pi*r^2\]
So, after combining like terms, and such, we should see
\[18\pi+6\pi*h=226.08\]
Now, solving for h should be some simple algebra.
\[h=(226.08-18\pi)/6\pi\]
\[h=8.999m\]
Or, 9meters.