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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.

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Solution

For cone, h = 3.6 cm, r = 1.6 cm

Volume of the given cone = 1/3 x Π 2 h = (1/3 x 22/7 x 1.6 x .16 x 3.6) cm2


Radius of the second cone = 1.2 cm. Let its height be h1</sup> then,

Volume of the second cone = 1/3 x Π r2 h = 1/3 x 22/7 x 1.2 x h1

it is melted and recasted so , the volume of the cones would be equal, therefore

1/3 x 22/7 x 1.2 x h1 = 1/3 x 22/7 x 1.6 x .16 x 3.6

h1 = (1.6 x 1.6 x 1.6) / (1.2 x 1.2) = 6.4

Hence the height of the second cone is 6.4 cm


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