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?
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'.
;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.
Muliply that by:
and you have:
3. Multiply the fraction by 2 and it does not match up with the volume for sphere. Why not?