Question

You have an ice cream scoop with a 2-inch diameter. You have an ice cream cone with a 2-inch diameter and a height of 5 inches. If you place one scoop of ice cream on the cone and let the ice cream melt, will it spill over the cone?

Answer 1

No, because the volume of the cone is greater than the volume of the ice cream scoop.

Explanation:

To solve this problem we just need to compare the volume of the ice scream scoop with the volume of the ice cream cone.

The ice scream scoop is a sphere with a diameter of 2 inches (so a radius of 1 inch), then the volume is:

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

V = (4/3) * pi * 1^3

V = 4.1888 in3

Now, to find the volume of the ice cream cone, we just need to use the formula of the cone volume (with radius = 1 inch):

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

V = (1/3) * pi * 1^2 * 5

V = 5.236 in3

As the volume of the cone is greater than the volume of the ice cream scoop, the ice cream will not spill over the cone after melting.