If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how much water flows out of the cylindrical cup
a. 38.8 cm³
b. 55.4 cm³
c. 19.4 cm³
d. 471.4 cm³

Solution:

Given, a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5 cm and height 6 cm.

We have to find the quantity of water that flows out of the cylindrical cup.

We know that when the marble is put inside the cylindrical cup full of water the volume of water displaced is equal to the volume of the marble.

So, volume of water that flows out = volume of the marble

Volume of sphere = (4/3)πr³

Given, radius = 2.1 cm

So, volume of marble = (4/3)(22/7)(2.1)³

= 38.808 cm³

Therefore, the volume of the water that flows out is 38.8 cm³

✦ Try This: If a steel ball of radius 1.2 cm is put into a cylindrical cup full of water of radius 7cm and height 3 cm, then how much water flows out of the cylindrical cup?

Given, radius of steel ball = 1.2 cm

Radius of cylindrical cup = 7 cm

Height of the cylindrical cup = 3 cm

Steel ball is put into a cylindrical cup full of water.

We have to find the quantity of water that flows out of the cylindrical cup.

We know that the quantity of water displaced is equal to the volume of the steel ball.

Volume of the steel ball = (4/3)πr³

= (4/3)(22/7)(1.2)³

= 7.241 cm³

Therefore, the quantity of water displaced is 7.241 cm³

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.1 Sample Problem 2

If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how much water flows out of the cylindrical cup a. 38.8 cm³, b. 55.4 cm³, c. 19.4 cm³, d. 471.4 cm³

Summary:

If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then quantity of water that flows out of the cylindrical cup is 38.8 cm³

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