Question

Metallic spheres each of radius 2 cm, are packed into a rectangular box of internal dimenshions 16 cm by 8 cm by 8 cm .When 16 spheres are packed ,the box is filled with preservative liquid . Find the volume of this liquid.

Answer 1

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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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