Marbles of diameter 1.4, cm are dropped into | vedclass

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(B) The volume of the water displaced in the cylindrical beaker is equal to the total volume of the submerged marbles.Radius of the beaker $R = \frac{

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(B) The volume of the water displaced in the cylindrical beaker is equal to the total volume of the submerged marbles.Radius of the beaker $R = \frac{7}{2} = 3.5\, cm$.Height of the water rise $h = 5.6\, cm$.Volume of raised water $= \pi R^2 h = \frac{22}{7} 	imes 3.5 	imes 3.5 	imes 5.6 = 215.6\, cm^3$.Radius of a marble $r = \frac{1.4}{2} = 0.7\, cm$.Volume of one marble $= \frac{4}{3} \pi r^3 = \frac{4}{3} 	imes \frac{22}{7} 	imes 0.7 	imes 0.7 	imes 0.7 = \frac{4}{3} 	imes 22 	imes 0.1 	imes 0.49 = \frac{4.312}{3}\, cm^3$.Let the number of marbles be $n$.$n 	imes (	ext{Volume of one marble}) = 	ext{Volume of raised water}$$n 	imes \frac{4.312}{3} = 215.6$$n = \frac{215.6 	imes 3}{4.312} = 50 	imes 3 = 150$.Therefore,$150$ marbles were dropped into the beaker.

Marbles of diameter $1.4\, cm$ are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is $7\, cm.$ Find how many marbles have been dropped in it if the water rises by $5.6\, cm.$

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