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There is water to a height of 14 cm in a cylindrical glass jar of radius 8 cm. Inside the water there is a sphere of diameter 12 cm completely immersed. By what height will the water go down when the sphere is removed?

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ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
The height and radius of a cylindrical glass jar is given which is having water in it.
Inside the water there is a sphere of given diameter completely immersed. By what height will the water go down when the sphere is removed?
This is the Question Number 16, Exercise 17.5 of M.L Aggarwal.

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1 Answer

  1. ML Aggarwal Sol Class 10 Maths chapter 17-43

    Given radius of the glass jar, R = 8 cm

    Diameter of the sphere = 12 cm

    Radius of the sphere, r = 12/2 = 6 cm

    When the sphere is removed from the jar, volume of water decreases.

    Let h be the height by which water level will decrease.

    Volume of water decreased = Volume of the sphere

    R2h = (4/3)r3

    82h = (4/3)63

    h = (4/3)×6×6×6/(8×8)

    = 18/4 = 9/2 = 4.5 cm

    Hence the height by which water level decreased is 4.5 cm.

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