Question:
glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm x 8 cm x 8 cm and then the box is filled with water. Find
the volume of water filled in the box.
Solution:
Given, dimensions of the cuboidal = 16 cm x 8 cm x 8 cm
Volume of the cuboidal = 16 x 8 x 8 = 1024 cm3
Also, given radius of one glass sphere = 2 cm
$\therefore \quad$ Volume of one glass sphere $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \times \frac{22}{7} \times(2)^{3}$
$=\frac{704}{21}=33.523 \mathrm{~cm}^{3}$
Now, volume of 16 glass spheres $=16 \times 33.523=536.37 \mathrm{~cm}^{3}$
$\therefore \quad$ Required volume of water $=$ Volume of cuboidal $-$ Volume of 16 glass spheres
$=1024-536.37=487.6 \mathrm{~cm}^{3}$