Metal sphere, each of radius 2 cm, are packed into a rectangular box of internal dimension `16 cm xx 8 cm xx 8 cm`. When 16 spheres are packed the box is filled with presrvative liquied .Find the volume of this liquid. Give your answer to the nerest interger. [ use `pi = 3.14`].

Explanation

Given, radius of each metal sphere = 2cm ,
Internal dimension of a rectangular box,
l= 16 cm, b= 8 cm , and h = 8 cm
`therefore` Volume of a metallic sphere `= (4)/(3)pir^(3) = (4)/(3) = xx3.14 xx (2)^(3)`
`= (4)/(3) xx 3.14 xx8`
Now, volume of 16 metallic spheres `= (4 xx 3.14 xx 8 xx16)/(3) = (100.48 xx 16)/(3)`
` = (1607.68)/(3) = 535.89 cm^(3)`
and internal volume of a rectangular box
`= lxx b xx h =16xx8xx8`
`=1024 cm^(3)`
`therefore` volume of preservative liquid = 1024-535.89
` = 488.11 ~~ 488 cm^(3)`
Hence, the volume of preservative liquid when 16 metallic spheres are packed in rectangular box is `488 cm^(3)`.