A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm.

Question:

A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height.

Solution:

Let the cone which is being melted be denoted by cone 1 and let the cone into which cone 1 is being melted be denoted by cone 2.

Height of cone 1 = 3.6 cm
Radius of the base of cone 1 = 1.6 cm
Radius of the base of cone 2 = 1.2 cm
Let h cm be the height of cone 2.
The volumes of both the cones should be equal

i. e.,$\frac{1}{3} \pi \times 1.6^{2} \times 3.6=\frac{1}{3} \pi \times 1.2^{2} \times \mathrm{h}$

$\Rightarrow \mathrm{h}=\frac{1.6 \times 1.6 \times 3.6}{1.2 \times 1.2}=6.4 \mathrm{~cm}$

∴ Height of cone 2 = 6.4 cm

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