We have a cylinder of radius a and height h. We need to prove its volume to be equal to pi*a^2*h using triple integral and spherical coordinates. The best way to solve this problem is to divide the cylinder to two volume regions , the first region is the one defined by phi to range from 0 to arctan(a/h) and the second region is the one defined by phi to range from arctan(a/h) till pi/2. Surley , for both regions theta will vary from 0 till 2*pi. However , i tried many times to find the proper limits for the radius for each region but i failed. So how do i properly define the radius for each region ?
Edit : I know the limits of each region for the radius r= 0 till asecθ and r= 0 till bcscθ but my question exactly is how to drive them ?