Question

Acubicalblock of edge 22cm is melted into small spherical balls of radius 1cm . Calculate the number of balls that can be made from it.

Answer 1

Edge of a cubical block = 22 cm
so, volume of cubical block = ${\left(22\mathrm{cm}\right)}^3=10648{\mathrm{cm}}^3$
Radius of each spherical ball = 1 cm
So volume of each small spherical ball = $\frac{4}{3}\pi {\mathrm{r}}^3=\frac{4}{3}\times \frac{22}{7}\times 1^3=\frac{88}{21}{\mathrm{cm}}^3$
So, number of spherical balls = $\frac{\mathrm{volume}\mathrm{of}\mathrm{cubical}\mathrm{block}}{\mathrm{volume}\mathrm{of}\mathrm{each}\mathrm{spherical}\mathrm{ball}}=\frac{10648}{{\displaystyle \frac{88}{21}}}=\frac{10648\times 21}{88}=2541$
Therefore the number os small spherical balls that can be made is 2541.