Question

16 glass spheres each of radius 2 cm are packed into 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.

Answer 1

Given, dimensions of the cuboidal = 16 cm × 8 cm × 8 cm

Volume of the cuboidal = 16 × 8 × 8 = 1024 cm³

Also, given radius of one glass sphere = 2 cm

∴ Volume of one glass sphere

= `4/3 pi"r"^3`

= `4/3 xx 22/7 xx (2)^3`

= `704/21`

= 33.523 cm³

Now, volume of 16 glass spheres

= 16 × 33.523

= 536.37 cm³

∴ Required volume of water

= Volume of cuboidal – Volume of 16 glass spheres

= 1024 – 236.37

= 487.6 cm³