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:

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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