Volume of sphere

Question

I know the formula of sphere and have seen number of derivations using with and without calculus.

I was using a common sense approach of using a slice and rotating this slice 360deg. Number of such slices would be 2(pi)(r) which is length of base circle of hemi-sphere. Then we can multiply the volume by 2 to get volume of entire sphere. I am using same logic as used for volume of a cylinder which is using a small slice and using number of such slices as height of the cylinder which is also its length.

What is wrong with my approach ?

Answer 1

As I see your slices cannot be considered as cylinders because they all meet at the center. So their width decrease to zero at the center. Just imagine that you have an internal sphere into you sphere. All slices will be convereted in the corresponding subslices with the smaller initial width on the surface.

Answer 2

Because of the way you slice the sphere.

Answer 3

Milly's comment :

The "thickness" of your "slice" is not uniform (thinner close to the center). This is not an issue with cylinders since slicing the cylinder you get "uniform thickness" for the slices.

I think this answers my question, so I am posting it as a self-answer. Because if we try to cut a slice from the exact center. The slice tapers into a corner resulting into obvious squeezing of thickness at the corner.