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.

Deepak BoraNewbie

# 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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Given radius of the glass jar, R = 8 cmDiameter of the sphere = 12 cmRadius of the sphere, r = 12/2 = 6 cmWhen 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 sphereR^{2}h = (4/3)r^{3}8^{2}h = (4/3)6^{3}h = (4/3)×6×6×6/(8×8)= 18/4 = 9/2 = 4.5 cmHence the height by which water level decreased is 4.5 cm.