Question

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π =3.14]

Answer 1

According to the question,

Radius of each sphere, r = 2 cm

Volume of a sphere is given by

Volume of 1 sphere = 4/3 πr³

Since there are 16 spheres in our question,

Volume of 16 spheres = 16 × 4/3 πr³

= 16 × 4/3 × 3.14 × 2³

= 535.89 cm³

We know that,

Dimensions of rectangular box = 16 cm × 8 cm × 8 cm

Volume of rectangular box = 16 × 8 × 8 = 1024 cm³

In order to find volume of the liquid that is filled in rectangular box,

We need to find the space left in the rectangular box after the space occupied by the spheres.

So, we can say that,

Volume of the liquid = (Volume of the rectangular box) – (Volume of the 16 spheres)

⇒ Volume of the liquid = 1024 – 535.89

= 488.11 cm³

Thus, volume of this liquid is 488.11 cm³.