Maths-
General
Easy

Question

A Solid consisting of a right circular cone , standing on a hemisphere , is placed upright , in a right circular cylinder , full of water and touches the bottom. Find the volume of the water left in the cylinder having given that the radius of the cylinder is 3 cm and its height is 6 cm, the radius of hemisphere is 2 cm and the height of the cone is 4 cm.Give your answer to the nearest cubic centimetre .

Hint:

Volume of cone equals 1 third pi r squared h
Volume of cylinder equals pi r squared h
Volume of hemisphere equals 2 over 3 pi r cubed

The correct answer is: 136cm3


    Explanation:
    • We have given right circular cone , standing on a hemisphere , is placed upright , in a right circular cylinder , full of water and touches the bottom.
    • We have to find d the volume of the water left in the cylinder having given that the radius of the cylinder is 3cm and its height is 6cm , the radius of hemisphere is 2cm and the height of the cone is 4cm.
    Step 1 of 1:
    We have
    Radius of cylinder 3cm
    Height of cylinder 6cm
    Radius of hemisphere 2cm
    Height of cone 4cm
    Volume of the water in the cylinder when it is full
    pi r squared h equals pi cross times 3 cross times 3 cross times 6 equals 54 pi cm cubed
    Volume of water displaced =volume of cone + volume of hemisphere.

    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 2 squared left parenthesis 4 plus 2 left parenthesis 2 right parenthesis right parenthesis
    equals 32 over 3 pi cm cubed
    Therefore, volume of water which is left

    equals 54 pi minus 32 over 3 pi

    equals 130 over 3 pi cm cubed

    = 136.19cm3

    = 136cm3

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