Originally Posted by

**icelated** I have a problem where i don't understand how the solutions manual is doing the steps.

Problem: Find the area of the zone of a sphere formed by revolving the graph of

$\displaystyle y = \sqrt 9 - x^2 , 0< x < 2 $ about the y axis. I think you meant this to be $\displaystyle y = \sqrt{9 - x^2}\, ,\ 0<x<2 $

so, $\displaystyle y = \sqrt 9 - x^2$

then, sorry the square root suppose to go over the whole equation.

$\displaystyle y \prime = \frac {-x} {\sqrt 9 - x^2} $

usually at this point it is $\displaystyle 1 + (y \prime)^2$

The solutions manual shows

$\displaystyle \sqrt 1 + (y \prime)^2$ Likewise, this should be $\displaystyle \sqrt{ 1 + (y \prime)^2}$

Why did they do this?

And the next step is confusing..

$\displaystyle \frac {3}{\sqrt 9 - x^2} $ Likewise, this should be $\displaystyle \frac {3}{\sqrt{ 9 - x^2}} $

Where did the 2 come from?

And in the next step where did the x come from?

$\displaystyle S = 2 \pi \int \frac {3x}{\sqrt 9 - x^2} dx$