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Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm

Solution:

Given, marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water.

We have to find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

Radius of marble = 1.4/2 = 0.7 cm

Volume of marble = (4/3)πr³

= (4/3)π(0.7)³

= 0.457π cm³

Given, radius of cylindrical beaker = 7/2 = 3.5 cm

Water level in the beaker has to rise by 5.6 cm

So, h = 5.6 cm

Volume of cylinder = πr²h

= π(3.5)²(5.6)

= 68.6π cm³

Number of marbles = volume of cylindrical beaker/volume of marble

= 68.6π/0.457π

= 68.6/0.457

= 150

Therefore, the number of marbles that should be dropped is 150.

✦ Try This: A sphere of radius 3cm is dropped into a cylindrical vessel of radius 4cm. If the sphere is submerged completely, then the height (in cm) to which the water rises, is

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

NCERT Exemplar Class 10 Maths Exercise 12.3 Problem 10

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm

Summary:

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. The number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm is 150

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