Maths-
General
Easy

Question

A Solid is in the form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 3.5 cm and height of the cone is 4 cm . The solid is placed in a cylindrical vessel , full of water , in such a way that the whole solid is submerged in water. If the radius of cylindrical vessel is 5 cm and its height is 10.5 cm . Find the volume of water left in the cylindrical vessel

hintHint:

Volume of hemisphere equals 2 over 3 pi r cubed

The correct answer is: 683.84cm3


    Explanation:
    • We have given a Solid is in the form of a right circular cone mounted on a hemisphere. The radius of hemisphere is 3.5 cm and height of the cone is 4 cm . The solid is placed in a cylindrical vessel , full of water , in such a way that the whole solid is submerged in water. If the radius of cylindrical vessel is 5 cm and its height is 10.5 cm
    • We have to find volume of water left in the cylindrical vessel.
    Step 1 of 1:
    We have given radius of the hemisphere is 3.5cm
    Now the solids is in the form of a right circular cone mounted on a hemisphere, then radius of the base  of the cone will be equal to radius of the hemisphere.
    Radius of the base of the cone is
    Height of the cone is
    So,
    Volume of the solid = volume of the cone + volume of hemisphere.
    So,

    V subscript text solid  end text end subscript equals 1 third pi r squared h plus 2 over 3 pi r cubed

    equals 1 third pi r squared left parenthesis h plus 2 r right parenthesis

    equals 1 third pi 3.5 squared left parenthesis 4 plus 7 right parenthesis

    = 141.109
    Now the radius of the base of the cylindrical vessel is 5cm
    Height of the cylindrical vessel is 10.5cm
    So, Volume of the water in the cylindrical vessel will be

    V equals pi r squared h

    equals 22 over 7 cross times 25 cross times 10.5

    = 825cm3
    Now, when the solid is completely submerged in the cylindrical vessel full of water,
    The
    Volume of the water left in the vessel = volume of the water in the vessel – volume of solid

    = (825 - 141.16)cm3

    = 683.84cm3

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