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Perfect Cone

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 implies πr2h = 300.

Curved surface area of cylinder = 2πrh = 150.

therefore
πr2h

2πrh
=
r

2
=
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

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