Marbles of diameters 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 beaker so that the water level rises by 5.6 cm.
Given,
Diameter of marble = 1.4 cm
Diameter of cylinder = 7 cm
Radius of cylinder = 3.5 cm
Cylinder height = 5.6 cm
Radius of marble = 0.7 cm
Volume of 1 marble = πr3
= = 1.4373
So,
Let the number of marbles be n,
Increase in the Volume of cylinder due to n marbles = πr2h
= 3.14 × 3.5 × 3.5 × 5.6 = 215.6 cm3
Hence the total numbers of marble required = = 150 marbles