A spherical scoop of ice cream is placed on top of a hollow ice cream cone. the scoop and cone have the same radius. the ice cream melts completely and it fills the cone to the top. how many times greater is the height of the cone than the radius of the cone?

The figure shown below illustrates the problem.

The volume of the empty cone is

V₁ = (1/3) π r²h

The volume of the sphere is

V₂ = (4/3) π r³

Because the melted ice cream completely fills the cone, therefore

V₁ = V₂

(1/3) π r² h = (4/3) π r³

Divide each side by (1/3) π r².

h = 4r

Answer:

The height of the cone is 4 times greater than the radius f the cone.