Q. 193.7( 3 Votes )
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
The volume of sphere =
Volume of cylinder = πr2h
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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