If a sphere of ice cream that was 2.5 inches in diameter was placed on top of the ice cream cone that had a height of 4 inches and a diameter of 1.75 inches and left to melt directly into the cone, would the all of the ice cream fit into the cone? Justify your answer using mathematics and a complete sentence answer.

The cone would not the all of the ice cream fit into the cone.

Step-by-step explanation:

Geometrically speaking, the volume of the cone (), measured in cubic inches, is described by the following equation:

(1)

Where:

- Base radius, measured in inches.

- Height, measured in inches.

And the ice cream ball is described by the volume equation for the sphere (), measured in cubic inches:

(2)

Where is the radius of the ice cream ball, measured in inches.

In this case, the ice cream will fit into the cone if and only if . That is:

If we know that , and , then the inequation is:

(CRASH!)

Which leads to an absurd. Hence, the cone would not the all of the ice cream fit into the cone.