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Question
Metal spheres each of radius 2cm are packed into a rectangular box of internal dimension 16cm x 8cm x 8cm when 16 spheres are packed the box is filled with preservative liquid. Find volume of this liquid?
Solution
Given radius of metal spheres = 2cm
Volume of sphere(v) = `4/3pir^3`
So volume of each metallic sphere =`4/3pi(2)^3cm^3`
Total volume of 16 spheres `(v_1)=16xx4/3pi(2)^3cm^3` ....(1)
Volume of rectangular box = lbh
V2 = 16 x 8 x 8cm3 .....(2)
Subtracting (2) – (1) we get volume of liquid
⇒ `V_2-V_1=`Volume off liquid
⇒ `16xx8xx8-4/3pi(2)^3xx16`
⇒ 1024 - 536.16 = 488cm3
∴Hence volume of liquid = 488cm3
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