Maths-
General
Easy

Question

A hemisphere of 5 cm radius surmounted by a right circular cone of 5 cm base radius. Find the volume of the solid correct to two places of decimals if the height of the cone is 7 cm.

Hint:

Volume of hemisphere
Volume of cone equals 1 third pi r squared h

The correct answer is: 445.05


    Explanation:
    • We have given a hemisphere of radius 5cm surmounted by a right circular cone of base radius 5cm.
    • We have to find the volume of the solid if the height of the cone is
    Step 1 of 1:
    The radius of a hemisphere is 5cm
    So, The volume of hemisphere will be

    V equals 2 over 3 pi r cubed

    equals 2 over 3 pi left parenthesis 5 right parenthesis cubed
    equals fraction numerator 250 pi over denominator 3 end fraction
    Volume of cone will be

    V equals 1 third pi r squared h

    equals 1 third pi left parenthesis 5 right parenthesis squared cross times 7
    equals fraction numerator 175 pi over denominator 3 end fraction
    Now the volume of solid will be equal to sum of volume of hemisphere and volume of the cone.
    So,

    equals fraction numerator 175 pi over denominator 3 end fraction plus fraction numerator 250 pi over denominator 3 end fraction

    equals fraction numerator 425 pi over denominator 3 end fraction

    = 445.05

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