Note that we have two equations that we can set up:

---------------[Volume of the cylinder]

-------[Surface area of cylinder]

I would first solve for height in the volume equation, and then substitute that into the surface area equation:

Subbing in, we see that

Now simply a little bit:

Thus,

Setting , we see that . Note that , where is the diameter of the base. Thus,

Now what is h?

Note that

Thus,

We have shown that the height and diameter are the same.

Does this make sense?

--Chris