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

Answer 1

volume of 16 spheres = (4/3 ×22/7 × 6 × 6 × 6)c.c=(6336/7)c.c=905·14c.c(apr.)
volume of the box = (16 × 8 × 8)c.c=1024c.c
∴volume of preservative liquid = (1024 - 905·14)c.c =118·86 c.c=119c.c(approx)

Answer 2

Answer:

The volume of the liquid is 488 cm³.

Step-by-step explanation:

Given :  

Radius of the metallic sphere, r  = 2 cm

Dimension of rectangular box = 16 × 8 × 8

Volume of the sphere = 4/3πr³

Volume of 16 spheres = 16 ×  4/3πr³

Volume of the 16 spheres = 64/3π(2)³ ……..(1)

Volume of the rectangular box= lbh = 16 × 8 × 8  cm³………………(2)

Volume of the liquid = Volume of a rectangular box - Volume of 16 spheres

= 16 × 8 × 8 - 64/3π(2)³

[From eq 1 & 2]

= 1024 - 64/3 × 22/7  × 8  

= 1024 - 11264/21

= 1024 – 536.38cm³

= 487.62 cm³ ≈  488 cm³

Volume of the liquid = 488 cm³

Hence,The volume of the liquid is 488 cm³

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