## Ice Cream Cone

#### Problem

An ice cream cone is packed full of ice cream and a generous hemisphere of ice cream is placed on top.

If the volume of ice cream inside the cone is the same as the volume of ice cream outside the cone, find the height of the cone.

#### Solution

Using the result that a cone occupies exactly 1/3 of a cylinder with equal base and height and a sphere occupies 2/3 of the cylinder it fits inside, the hemisphere must have the same volume as 1/3 of the cylinder, i.e. the same volume as the cone.

That is the cone is twice the height of the hemisphere.

Hence the height of cone is 8 cm.

Problem ID: 71 (Mar 2002) Difficulty: 2 Star