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

Given, radius of each metal sphere = 2 cm

So, volume of a metallic sphere = `4/3 pir^3`

= `4/3 xx 3.14 xx (2  cm)^3`

= `100.48/3 cm^3`

= 33.49 cm³

Now, the volume of 16 such a sphere = 16 × 33.49 cm³ = 535.84 cm³ 

Dimensions of internal box is 16 cm × 8 cm × 8 cm.

Now, internal volume of a rectangular box = 16 cm × 8 cm × 8 cm = 1024 cm³

Volume of the preservative liquid = 1024 cm³ – 535.84 cm³ = 488.16 cm³