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Question

A right circular cone is 5.8cm high and radius of its base is 3.4cm. It is melted and recast into a right circular cone with radius of its base 1.7cm. Find its height.

A
20.2cm
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B
21.2cm
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C
23.2cm
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D
22.2cm
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Solution

The correct option is C 23.2cm
Given, height of cone1= h1=5.8 cm
and the radius of the base r1=3.4 cm

Also, the radius of the base of second cone r2=3.4 cm
Let the height of the second cone be h

Given: Volume of cone1= Volume of cone2

13πr21h1=13πr22h2

13×π×(3.4)2×5.8=13×π(1.7)2×h

h=(3.4)2×5.8(1.7)2

=23.2 cm

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