Question

A cone is inscribed in a sphere with a radius of 5 centimeters.The distance from the center of the sphere to the center of the base of the cone is x. Write an expression for the volume of the cone in terms of x (Hint: Use the radius of the sphere as part of the height of the cone)

Help would be so very appreciated! Thanks beforehand! (:

Answer 1

If the base of the cone is x units below the center of the sphere,

cone height = x+5

Draw a line from the center of the sphere to the base of the cone. It is a radius, so its length is 5.

If the radius of the base of the cone is r, the

r^2 + x^2 = 25
r^2 = 25-x^2

volume of cone is

v = 1/3 pi r^2 * h = 1/3 pi (25-x^2)(x+5)