A large waffle cone has a height of 7.25 inches and a radius of 1.5 inches. Two scoops of sorbet are placed on the wide end of the cone. The scoops are spheres with a radius of 1.5 inches. If all the sorbet melts into the cone, will the cone overflow? Show all of your work.

Answer 1

To determine if the cone will overflow, we need to find the volume of the cone and the volume of the sorbet.

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

Substituting the given values, we get:

V_cone = (1/3)π(1.5^2)(7.25)

V_cone ≈ 15.31 cubic inches

The volume of a sphere is given by the formula V = (4/3)πr^3.

Since we have two scoops of sorbet, we need to find the total volume by doubling the volume of a single scoop:

V_sorbet = 2[(4/3)π(1.5^3)]

V_sorbet ≈ 14.14 cubic inches

So the total volume of the cone and the sorbet is:

V_total = V_cone + V_sorbet

V_total ≈ 29.45 cubic inches

Since the total volume is less than the volume of the cone alone, the sorbet will not cause the cone to overflow.