Question

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 ​

Answer 1

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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