Maths-
General
Easy

Question

What is the least number of solid metallic spheres of 6 cm diameter that should be melted and recast to form a solid metal right circular cone whose height is 135 cm and diameter is 4 cm?

hintHint:

Volume of sphere 4 over 3 pi r cubed

The correct answer is: 5


    Explanation:
    • We have given solid metallic spheres of 6 cm diameter that should be melted and recast to form a solid metal right circular cone whose height is 135 cm and diameter is 4 cm
    • We have to find the least number of those sphere.
    Step 1 of 1:
    Let the number of solid metallic sphere be n
    Volume of one sphere be

    V equals 4 over 3 pi left parenthesis 3 right parenthesis cubed
    equals 36 pi
    Volume of metallic cone will be

    equals 1 third pi cross times 2 squared cross times 135
    equals 180 pi
    Now,

    n equals fraction numerator text  Vol of metal cone  end text over denominator text  Volume of sphere  end text end fraction

    n equals fraction numerator 180 pi over denominator 36 pi end fraction

    n = 5
    So, The least number of sphere needed to form the cone is 5.

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