The radius of the base of a cone is x cm and its height is h cm.
The radius of a sphere is 2x cm.
The volume of the cone and the volume of the sphere are equal.
Express h in terms of x.
Give your answer in its simplest form.
Vcone = (1/3)8pi * r^2 * h
Vsphere = (4/3) * pi * r^3
So
(1/3)*pi * (x)^2 * h = (4/3) * pi * (2x)^3 divide through by pi
(1/3) * (x)^2 * h = (4/3) * (2x)^3 multiply through by 3
(x)^2 * h = 4 * (2x)^3 simplify
x^2 * h = 32x^3 divide through by x^2
h = 32x
Volume of sphere=4/3.Pi.(2x)^3=Volume of cone=Pi.x^2.(h/3)
4/3*Pi*(2x)^3=Pi*x^2*(h/3)
