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?

Answer 1

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