Question

Suppose a sphere and a cone share the same radius and the height of the cone is twice the radius. Which ratio describes the relationship between the formulas for the volume of a cone to the volume of a sphere?(

Answer 1

The volume formula of a sphere is V = (4/3)πr^3, where r is the radius.
The volume formula of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.

Given that the height of the cone is twice the radius, we can substitute 2r for h in the cone volume formula:

V_cone = (1/3)πr^2(2r) = (2/3)πr^3

Therefore, the ratio of the volume of the cone to the volume of the sphere is:

V_cone : V_sphere = (2/3)πr^3 : (4/3)πr^3 = 2:4 = 1:2