Question

Mearbles 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.

Answer 1

Given , diameter of a marble = 1.4 cm
`therefore` Radius of marble `= (1.4)/(2) = 0.7 cm`
So, volume of one marble `= (4)/(3 pi (0.7)^(3)`
`=(4)/(3) pi xx 0.343= (1.372)/(3) pi cm^(3)`
Also, given diameter of beaker = 7 cm
`therefore ` Radius of beaker `=(7)/(2) = 3.5 cm`
Height of water level raised water in beaker `= pi (3.5)^(2) xx 5.6 = 68.6 pi cm^(3)`
Now, required number of marbles `= ("Volume of the raised water in beaker")/("Volume of one spherical marble")`
`=(68.6pi)/(1.372 pi) xx 3=150`