Metal spheres, each of the radius 2 cm, are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid.
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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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