Q19 of 51 Page 13

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.

Given: Diameter of marble = 1.4 cm


Diameter of cylindrical beaker = 7 cm


Height of water level = 5.6 cm


Formula used:


The volume of sphere =


Volume of cylinder = πr2h


Explanation:


diameter of a marbles = 1.4 cm


∴ Radius of marble = = 0.7 cm


So, volume of one marble =





Also, given diameter of beaker = 7 cm


∴ Radius of beaker = = 3.5 cm


Height of water level raised = 5.6 cm


∴ Volume of the raised water in beaker = π r2 h


= π (3.5)2 × 5.6


= 68.6 π


Let n marbles be dropped into the beaker,


Hence n × volume of marble = volume of water raised


⇒


⇒


⇒ n = 150


Hence the number of marbles required are 150.


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