Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 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]

Given: radius of each sphere, r = 2 cm

Then, volume of a sphere is given by


Volume of 1 sphere = 4/3 πr3


There are 16 spheres.


So, volume of 16 spheres = 16 × 4/3 πr3


= 16 × 4/3 × 3.14 × 23


= 535.89 cm3


Volume of rectangular box = 16 × 8 × 8 = 1024 cm3 [∵, dimensions of rectangular box = 16 cm × 8 cm × 8 cm]


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, 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.


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