ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 14 Mensuration Exercise 17.5

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?



When the sphere is removed than the amount of water decreased will be equivalent to the volume of the sphere.

M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Mensuration Question 14 Solution image

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

π R2h = (4/3)π 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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