Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water .Then the number of marbles that should be dropped into the beaker so that the water level Rises by 5.6 cm is
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Diameter of marble =1.4cm
Therefore,
radius of marble =1.4/2=0.7cm
Volume of 1 marble =4/3πr³=4/3×π×(0.7)³.....(1)
Now,
Diameter of beaker =7cm
Therefore,
radius of beaker =7/2=3.5cm
Height of water =5.6cm
Volume of water =πr²h=π×(3.5)²×5.6.....(2)
Now,
No. of marbles dropped =Volume of 1 marble/Volume of water
⇒ No. of marbles dropped =π×(3.5)²×5.6/4/3×π×0.7³
⇒ No. of marbles dropped =150
Hence 150 marbles have been dropped in the beaker.
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