Question

Question 11
16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions $16cm\times 8cm\times 8cm$ and then the box is filled with water. Find the volume of water filled in the box

Answer 1

Given dimensions of the cuboidal $=16cm\times 8cm\times 8cm$

$\therefore$ Volume of the cuboidal $=l\times b\times h=16\times 8\times 8=1024c{m}^3$

Also, given radius of one glass sphere = 2 cm

$\therefore$ Volume of one glass sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (2{)}^3$

$=\frac{704}{21}=33.523c{m}^3$

Now, volume of 16 glass spheres $=16\times 33.523=536.37c{m}^3$

$\therefore$ Required volume of water = Volume of cuboidal – Volume of 16 glass spheres

$=1024-536.37=487.6c{m}^3$