# 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?

Solution:

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

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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