Question

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16cm x 8cm x 8cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid (in $c{m}^3$). Give your answer to the nearest integer. [Use $\pi =3.14$]

Answer 1

Volume of rectangular box$=lbh=16\left(64\right)=1024c{m}^3$
Volume of sphere$=\frac{4}{3}\pi r^3=33.5238c{m}^3$
16 sphere$=16\left(33.5238\right)=536.3808$
Volume of liquid$=1024-536.3808=488c{m}^3$