Question

Question 10
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.

Answer 1

Given, diameter of a marble = 1.4 cm
$\therefore Radiusofmarble=\frac{1.4}{2}=0.7cm$
So, volume of one marble $=\frac{4}{3}\pi (0.7{)}^3\frac{4}{3}\pi \times 0.343=\frac{1.372}{3}\pi c{m}^3$
Also given diameter of beaker = 7 cm
$\therefore$ Radius of beaker $=\frac{7}{2}=3.5cm$
Height of water level raised = 5.6 cm
$\therefore$ Volume of the raised water in breaker
$=\pi (3.5{)}^2\times 5.6=68.6\pi c{m}^3$
Now, required number of marbles $=\frac{Volumeofraisedwaterinbeaker}{Volumeofonesphericalmarble}$
$=\frac{68.6\pi }{1.372\pi }\times 3=150$