need to find radius of cylinder, given height, surface area

[sparky14761]

How to solve this?

The surface area of a right cylinder is 324.7 (pi) square meters. Find the radius of the base of the cylinder if the height of the cylinder is 5.6 meters.

What I did so far is...
2(pi)(r)5.6 + 324.7 (pi)
324.7 = 11.2r + 2r2
Then, what do I do find the radius?

 

[soroban]

Re: need your help

Hello, sparky14761!

The surface area of a right cylinder is \(\displaystyle 324.7\pi\) square meters.
Find the radius of the base of the cylinder if the height of the cylinder is 5.6 meters.

Your equation is fine: \(\displaystyle \,2r^2\,+\,11.2r\,-\,324.7\;=\;0\)

It's a quadratic . . . Use the Quadratic Formula:

\(\displaystyle \;\;r\;=\;\frac{-11.2\,\pm\,\sqrt{11.2^2\,-\,4(2)(-324.7)}}{2(2)}\;=\;\frac{-11.2\,\pm\,\sqrt{2723.04}}{4} \;= \;\frac{-11.2\,\pm\,52.18275577}{4}\)

And the positive root is: \(\displaystyle \,r\:\approx\:10.25\) meters.