Cylinder Surface Area as a Function of its Radius

Hi guys,

I've got two questions relating to surface area of a cylinder. Here they are:

1. Given that the volume of a cylinder is 405 cubic units, find an equation for the surface area in terms of its radius.

2. Graph the surface area against the radius.

My attempt:

Question 1:

I know the surface area of a cylinder includes its two circles as well as the rectangular part, giving the surface area to be $\displaystyle 2\pi r(r+h)$. The height in terms of the radius when volume is given is:

http://screensnapr.com/e/optcTq.jpg

When I sub this into the surface area equation, I get this:

http://screensnapr.com/e/1aRtE0.jpg

I'd like confirmation on whether this is right. The graph of it looks quite strange (I'm supposed to find the minimum from this). Thanks in advanced.

P.S. How come the pi doesn't show up in the tex tags?

Re: Cylinder Surface Area as a Function of its Radius

It looks fine. To get pi in the tex tags, you need to write \pi.