Question

Volume of the cone is equal to that of a sphere.If the diameter of base of cone is equal to the diameter of the sphere,what is the ratio of height of cone to the diameter of the sphere?

Answer 1

Answer:

Since diameter of base of cone is equal to diameter of sphere.

Then, radius of base of cone will be equal to radius of sphere.

Volume of cone =Volume of sphere

=(1/3)πr²h = (4/3)πr³

=h=4r

Thus,

h/diameter

=h/2r

=4r/2r

=2/1

=2:1

Thus, ratio of height of cone to the diameter of sphere is 2:1