Metal spheres, each of the radius 2 cm, are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid.
The radius of each of the metallic sphere is 2cm. Therefore, the volume of each metallic sphere is
$V=\frac{4}{3} \pi \times(2)^{3} \mathrm{~cm}^{3}$
The total volume of the 16 spheres is
$V_{1}=16 \times \frac{4}{3} \pi \times(2)^{3} \mathrm{~cm}^{3}$
The internal dimension of the rectangular box is $16 \mathrm{~cm} \times 8 \mathrm{~cm} \times 8 \mathrm{~cm}$. Therefore, the volume of the rectangular box is
$V_{2}=16 \times 8 \times 8 \mathrm{~cm}^{3}$
Therefore, the volume of the liquid is
$V_{2}-V_{1}=16 \times 8 \times 8-16 \times \frac{4}{3} \pi \times(2)^{3}$
$=1024-536.03$
$=488$
Hence volume of liquid is $488 \mathrm{~cm}^{3}$