volume of the sphere is given by V = 4/3Pi r^3
proof
Find the volume formed by revolving the circle given by r^2 = x^2 + y^2 about the x-axis
usig disk method
limits are [r,-r].............. where r = radius
from V=pi ∫R(x)^2 dx
given r^2 = y^2 + x^2....................x = {r^2 - y^2}^1/2
V = pi ∫({r^2 - y^2}^1/2) dy
V = pi ∫(r^2 - y^2) dy ....... [r,-r]
V = pi(yr^2 - y^3/3) .......... [r,-r]
V = pi{ (r^3 - r^3/3) - (-r^3 + r^3/3) }
V = pi(2/3r^3 + 2/3r^3)
V = pi(4/3r^3)
V = 4/3pir^3,............ "hence proved"