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Maths-

General

Easy

Question

The radius of the base of a circular cone Is halved. Keeping the height same , What is the ratio of the volume of the reduced cone to that of the original cone ?

hint Hint:

Volume of the cone is $equals 1 third pi r squared h$

The correct answer is: 1/8

Explanation:

We have given the radius of the base of a circular cone Is halved. Keeping the height same

We have to find ratio of the volume of the reduced cone to that of the original cone

Step 1 of 1:
Let the radius of the cone initially be r
The radius of new reduced cone will be $r over 2$
The volume of original cone initially is $V subscript o equals 4 over 3 pi r cubed$
And the volume of reduced cone is
$V subscript r equals 4 over 3 pi open parentheses r over 2 close parentheses cubed$
$equals 1 over 8 cross times 4 over 3 pi r cubed$
So, the ratio will be
$V subscript r over V subscript o equals fraction numerator 1 over 8 cross times 4 over 3 pi r cubed over denominator 4 over 3 pi r cubed end fraction$
$V subscript r over V subscript o equals 1 over 8$

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