A spherical scoop of ice cream has the same radius as the base of a cone. The heights of the cone and the scoop of ice cream are the same.

If the sphere of ice cream were to melt, then how many ice cream cones of this type could it fill?

Guest Jun 26, 2020

#1**0 **

Since the height of the cone is the same as the hieght of the scoop of ice cream, the height of the

cone = 2r, where r is the radius of both the cone and the sphere of ice cream.

The volume of the sphere: V = (4/3)·pi·radius^{3} = V = (4/3)·pi·r^{3}

The volume of the cone: V = (1/3)·pi·radius^{2}·(height) = (1/3)·pi·r^{2}·(2r) = (2/3)·pi·r^{3}

The volume of the sphere is twice the volume of the cone, so it can fill two cones.

geno3141 Jun 26, 2020