 # Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. `
Question:

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.

Solution:

Diameter of each marble $=1.4 \mathrm{~cm}$

Radius of each marble $=0.7 \mathrm{~cm}$

Volume of each marble $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times(0.7)^{3} \mathrm{~cm}^{3}$

The water rises as a cylindrical column.

Volume of cylindrical column filled with water $=\pi r^{2} h=\pi \times\left(\frac{7}{2}\right)^{2} \times 5.6 \mathrm{~cm}^{3}$

Total number of marbles

$=\frac{\text { Volume of cylindrical water column }}{\text { Volume of marble }}$

$=\frac{\pi \times\left(\frac{7}{2}\right)^{2} \times 5.6}{\frac{4}{3} \pi \times(0.7)^{3}}$

$=\frac{7 \times 7 \times 5.6 \times 3}{2 \times 2 \times 4 \times 0.7 \times 0.7 \times 0.7}$

$=150$