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Question

If the radius of the base of a right circular cone is halved, keeping the height same, then the ratio of the volume of the reduced cone to that of the original cone is
  1. 2:1
  2. 4:1
  3. 1:4
  4. 1:2

A
1:4
B
2:1
C
4:1
D
1:2
Solution
Verified by Toppr

Suppose that

Radius of the base is r, and the height of the original cone is h.

Then,

Volume of the original cone (V1)=13πr2h

When cone reduced then,

radius =r2

height =h

Now,

Volume of the reduced cone (V2)=13π(r2)2h

=14(13πr2h)

=14V1$

V2V1=14=1:4

This is the required solution.

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