21 glass spheres, each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and, then the box is filled with water. Find the volume of water filled in the box.
It is given that 21 glass spheres each of radius 2 cm are packed in a cuboidal box of inner dimensions and then filled with water.
We have to find the volume of water.
Radius of glass sphere r
Volume of a glass sphere $=\frac{4}{3} \pi r^{3}$
Volume of 21 glass spheres $=21 \times \frac{4}{3} \times \frac{22}{7} \times 2^{3}$
$=21 \times \frac{4}{3} \times \frac{22}{7} \times 8$
$=704 \mathrm{~cm}^{3}$
Length of cuboidal box
Breadth of cuboidal box
Height of cuboidal box
Volume of the cuboidal box $=$ length $\times$ breadth $\times$ height
$=16 \times 8 \times 8$
$=1024 \mathrm{~cm}^{3}$
Volume of water = Volume of cuboidal box − Volume of glass spheres
$=1024-704$
$=320 \mathrm{~cm}^{3}$