## Perfect Cone

#### Problem

A cone is designed so that it fits perfectly into a cylindrical container.

Given the volume of the cone is 100 cm^{3} and the curved surface area of the cylinder is 150 cm^{2}, what is the height of the container?

#### Solution

Volume of cone = ^{1}/_{3} π`r`^{2}`h` = 100 π`r`^{2}`h` = 300.

Curved surface area of cylinder = 2π`rh` = 150.

π r^{2}h2π rh | = | r2 | = | 300 150 | = 2 | Þ r = 4 cm. |

Given that 2πrh = 150, we get 8πh = 150, hence h = | 75 4π | . |

Problem ID: 203 (24 Jan 2005) Difficulty: 2 Star