Here's my question:

Find the area of the surface created by the complete curve r=a when it is completely revolved about the x axis.Do not assume the formula for the surface area of a sphere.
Just by looking at it I did:

Mr F says: *Ahem* You're rotating a circle around the x-axis. This gives a sphere. You do recall that the surface area of a sphere is $\displaystyle {\color{red}4 \pi r^2}$, don't you?
Which was incorrect.

Mr F says: Obviously.
So then I did it the way I think I was supposed to:

and this answer was also wrong. The book gave the answer as:

What's going wrong??