The mass of any of the discs d M is the mass of the sphere M multiplied by the ratio of the volume of an infinitely thin disc divided by the volume of a sphere (with constant radius a ). The volume of an infinitely thin disc is π π R 2 d x , or π π ( a 2 − − x 2 ) d x . So, d M = π π M ( a 2 − − x 2 ) d x 4 3 π π a 3 . Simplifying gives d M = 3 M ( a 2 − − x 2 ) d x 4 a 3 .