2. A scoop of ice cream in the shape of a whole perfect sphere sits in a right cone.

The radius of the ice cream scoop is 2.5cm and the radius of the cone is 2.5cm.

How tall must the height of the cone be to fit all the ice cream without spilling if it melts?

Answer (Show Work) :

10 cm.

Step-by-step explanation:

The volume of the cone must be equal to the volume of the sphere for there to be no spillage.

The volume of the sphere = 4/3 π r^3 cm^3

= 4/3 * 2.5^3 π cm^3

The volume of the cone = 1/3 π 2.5^2 h where h is the height of the cone.

So: 4/3 * 2.5^3 π = 1/3 π 2.5^2 h

h = (4/3 * 2.5^3) π / (1/3 * 2.5^2) π

= 4 * 2.5

= 10 cm.