how to derive volume of cylinder and sphere using triple integral and double integral?.....?

Question

i was to derive the volume of cylinder using the incremental volume of a cube in a cylinder or sphere...right now the topics i will be on is triple integration in spherical and cylindrical coordinates....so probably it deals with values G(theta,radius,Z) and f(rho,theta,phi) coordinates, it also deals with integral limits....can anyone help me out? it would be of great help,thnx.

Answer 1

To set up the triple integral using cylindrical coordinates, let dV = rdθdrdh
The integral is then
R H 2π
∫ . ∫ . ∫rdθdrdh
0 0 0

There are 3 ways to set up the double integral, again in cylindrical coordinates. I think the easiest is
. . R 2π
H ∫ . ∫rdrdθ
. 0 0