Marbles of diameter 1.4 ,cm are dropped into | vedclass

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(A) Given,diameter of a marble $= 1.4 \,cm$.$	herefore$ Radius of a marble $(r) = \frac{1.4}{2} = 0.7 \,cm$.Volume of one spherical marble $= \frac{4

Vedclass · Accepted Answer

$150$

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(A) Given,diameter of a marble $= 1.4 \,cm$.$	herefore$ Radius of a marble $(r) = \frac{1.4}{2} = 0.7 \,cm$.Volume of one spherical marble $= \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.7)^3 = \frac{4}{3} \pi (0.343) = \frac{1.372}{3} \pi \,cm^3$.Given,diameter of the cylindrical beaker $= 7 \,cm$.$	herefore$ Radius of the beaker $(R) = \frac{7}{2} = 3.5 \,cm$.Height of the water level raised $(h) = 5.6 \,cm$.Volume of the water displaced (raised) in the beaker $= \pi R^2 h = \pi (3.5)^2 (5.6) = \pi (12.25) (5.6) = 68.6 \pi \,cm^3$.Let the number of marbles be $n$.Then,$n 	imes (	ext{Volume of one marble}) = 	ext{Volume of raised water}$.$n 	imes \frac{1.372}{3} \pi = 68.6 \pi$.$n = \frac{68.6 	imes 3}{1.372} = \frac{205.8}{1.372} = 150$.Thus,$150$ marbles are required.

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 $5.6 \,cm$.

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