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Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

Solution:

Given, diameter of spherical ball = 4.2 cm

We have to find the amount of water displaced by a spherical ball when it is completely immersed in water.

By Archimedes principle,

A body at rest in a fluid is acted upon by a force pushing upward called the buoyant force, which is equal to the weight of the fluid that the body displaces. If the body is completely submerged, the volume of fluid displaced is equal to the volume of the body.

Amount of water displaced = volume of solid spherical ball

Volume of sphere = 4/3 πr³

Where, r is the radius of sphere

Given, r = 4.2/2 = 2.1 cm

Volume = 4/3 (22/7)(2.1)³

= (4 × 22 × 2.1 × 2.1 × 2.1) / (3 × 7)

= (88 × 2.1 × 2.1 × 0.3) / 3

= 88 × 2.1 × 0.7 × 0.3

= 38.81 cm³

Therefore, the volume of water displaced is 38.81 cm³

✦ Try This: Find the amount of water displaced by a solid spherical ball of diameter 5 cm, when it is completely immersed in water.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.3 Problem 3

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

Summary:

The amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water is 38.81 cm³

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