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Question

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is 127 of the volume of the given cone, at what height above the base is the section made?


A
10 cm
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B
20 cm
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C
40 cm
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D
15 cm
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Solution

The correct option is B 20 cm
Given,
Height of original cone, H=30 cm
Let, Radius of original cone =R
Height of new cone =h
Radius of new cone =r

Volume of original cone
=13πR2H=13πR2×30=10πR2 cm3

Volume of the new cone formed
=13πr2h

Given, volume of the new cone is 127 times the volume of the original cone.
13πr2h=127×10πR2h=3027R2r2h=109(Rr)2

Also, from similarity of triangles, Rr=30h

h=109×(30h)2h×h2=10×9009h3=10×100h=310×10×10h=10 cm

The height at which the section is made is 20 cm above the base.

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