Question

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions $16\mathrm{cm}\times 8\mathrm{cm}\times 8\mathrm{cm}$ and then the box is filled with water . Find the volume of the water filled in the box .

Answer 1

Radius of the glass spheres, r = 2 cm
Dimensions of the cuboidal box = $16\mathrm{cm}\times 8\mathrm{cm}\times 8\mathrm{cm}$
volume of the spheres = $V_s=\frac{4}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3=\frac{4}{3}\mathrm{\pi }{\left(2\right)}^3$
volume of the cuboidal box = $V_c=16\times 8\times 8=1024$
Volume of water in the cuboidal box = Volume of the cuboidal box − Volume of the 16 glass spheres
$$\begin{gathered} =1024-16\times \frac{4}{3}\mathrm{\pi }{\left(2\right)}^3 \\ =1024-536.6 \\ =487.6{\mathrm{cm}}^3 \end{gathered}$$
Hence, the volume of the water in the cuboidal box = 487.6 cm³