The volume/SA of a sphere

I decided to abide by logic in order to reconstruct the formula for the volume of a sphere. Juxtapose against the actual formula, my formula does not match.

Why is it so?

My reasoning:

Let r be the radius of a circle.

1. I first use 'r' to find its 90 degree sector (is this how you would express finding a particular sector of a circle?), then I have area 'x'.

$\displaystyle \frac {90}{360} = \frac {x}{(\pi)r^2}$ ;where x is the area of the sector.

2. If I take x, or its equivalent fraction, and multiply it by the circumference of the circle with the radius of 'r' I should get the volume of half the sphere.

$\displaystyle \frac {90}{360} = \frac {x} {(\pi)r^2} $ simplifies to

$\displaystyle \frac {(\pi)r^2}{4}$

Muliply that by:

$\displaystyle

\pi2r

$

and you have:

$\displaystyle

\frac {\pi^2r^3}{2}

$

3. Multiply the fraction by 2 and it does not match up with the volume for sphere. Why not?