Question

An ice cream cone has a height of 6 inches and a radius of 2 inches. A scoop of ice cream sits on the top of the cone. The scoop is a sphere with a diameter of 4 inches. If the entire scoop of frozen yogurt melts into the cone, will the cone overflow? Show all your work and explain your reasoning.

Answer 1

Yes, it will overflow, because the volume of the scoop of ice cream is higher than the volume of the cone.

Explanation:

To know if the cone will overflow when the entire scoop of frozen yogurt melts, we need to compare the volume of the scoop and the volume of the cone: if the volume of the scoop is higher, it will overflow.

The volume of the cone is:

V_cone = (1/3)*pi*r^2*h

Where V_cone is the volume, r is the radius and h is the height. So:

V_cone = (1/3)*pi*2^2*6 = 25.1327 in3

The volume of a sphere is:

V_sphere = (4/3)*pi*r^3

Where V_sphere is the volume and r is the radius. If the diameter is 4, the radius is 4/2 = 2. So:

V_sphere = (4/3)*pi*2^3 = 33.5103 in3

The volume of the sphere is higher, so the cone will overflow.