mathschallenge.net

Problem

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

Given the volume of the cone is 100 cm³ and the curved surface area of the cylinder is 150 cm², what is the height of the container?

Solution

Volume of cone = ¹/₃ πr²h = 100 πr²h = 300.

Curved surface area of cylinder = 2πrh = 150.

πr2h 2πrh

=

r 2

=

300 150

= 2

Þ r = 4 cm.

Given that 2πrh = 150, we get 8πh = 150, hence h =

75 4π

.