Maths-
General
Easy

Question

An inverted conical vessel of 6 cm radius and 8 cm height is completely filled with water. A Sphere is lowered into the water and its size is such that when it touches the sides , it is just immersed. What fraction of water overflows ?

Hint:

Volume of sphere is 4 over 3 pi r cubed.
Volume of the cone is 1 third pi r squared h.

The correct answer is: 0.66


    Explanation:
    • We have given an inverted conical vessel of  radius and  height is completely filled with water. A Sphere is lowered into the water and its size is such that when it touches the sides , it is just immersed.
    • We have to find the fraction of water flow.
    Step 1 of 1:
    The conical vessel of radius 6cm and height 8cm
    The volume of cone

    V equals 1 third pi r squared h

    equals 1 third pi left parenthesis 6 right parenthesis squared cross times 8
    equals 301.59 cm cubed
    Since the sphere touches the cone, then
    Radius of sphere = radius of cone = 6cm

    V equals 4 over 3 pi r cubed

    equals 4 over 3 pi left parenthesis 6 right parenthesis cubed
    equals 904.77 cm cubed
    The volume of water flow will be

    equals 904.77 cm cubed minus 301.59 cm cubed

    = 603.18cm3
    So, The fraction will be

    equals fraction numerator 603.18 over denominator 904.77 end fraction

    = 0.66

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