Question

Metal spheres, each of radius $2cm$ are packet into a rectangle box of dimension $16cm\times 8cm\times 8cm$. When $16$ spheres are packed, the box is filled with preservative liquid Find the volume of the liquid.

Answer 1

Volume of one sphere $=\frac{4}{3}\pi \left(r^3\right)=\frac{4}{3}\pi 2^3=\frac{32}{3}\pi c{m}^3$

Volume of Rectangle box $=l\times b\times h=16\times 8\times 8=1024c{m}^3$

Volume of liquid $=1024-\frac{32}{3}\pi \times 16=487.83c{m}^3$