Maths-
General
Easy

Question

A hemispherical container of 4 cm radius is filled to the brim with milk . The milk is then poured in a vertical right circular cone of 8 cm radius and 16 cm height. What percentage of the vertical right circular cone remains empty ?

Hint:

Volume of hemisphere equals 2 over 3 pi r cubed

The correct answer is: 87.5%


    Explanation:
    • We have given A hemispherical container of 4 cm radius is filled to the brim with milk . The milk is then poured in a vertical right circular cone of 8 cm radius and 16 cm height.
    • We have to find What percentage of the vertical right circular cone remains empty.
    Step 1 of 1;
    Volume of hemispherical cone

    equals 2 over 3 pi r cubed

    equals 2 over 3 pi left parenthesis 4 right parenthesis cubed
    equals fraction numerator 128 pi over denominator 3 end fraction
    Volume of the cone

    equals 1 third pi r squared h

    equals 1 third pi left parenthesis 8 right parenthesis squared cross times 16
    equals fraction numerator 1024 pi over denominator 3 end fraction
    Volume of the cone remain empty

    equals fraction numerator 1024 pi over denominator 3 end fraction minus fraction numerator 128 pi over denominator 3 end fraction
    equals fraction numerator 896 pi over denominator 3 end fraction
    Percent of the cone empty

    equals fraction numerator fraction numerator 896 pi over denominator 3 end fraction over denominator fraction numerator 1024 pi over denominator 3 end fraction end fraction cross times 100 straight percent sign
    equals 87.5 percent sign

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