Question

Metal spheres, each of radius $2cm$, are packed into a rectangular box of internal dimension $16cm\times 8cm\times 8cm$ when $16$ spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. (Use $\pi =\frac{669}{213}$)

Answer 1

Volume of liquid $=$ Volume of box $-$volume of spheres

Hence $V=16\times 8\times 8-16(\frac{4}{3}\times \pi \times 2^3)$

$=16(64-\frac{32\pi }{3})=487.96c{m}^2$