Question

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions $6cm\times 42cm\times 21cm$.

Answer 1

Volume of rectangular lead piece $=lbh=6\times 42\times 21=5292c{m}^3$

Radius of each lead shot $=\frac{4.2}{2}=2.1cm$

Volume of each lead shot $=\frac{4\pi }{3}{r}^3=\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1=38.808c{m}^3$

So, number of leadshots that can be obtained $=\frac{Volumeofrectangularleadpiece}{Volumeofeachleadshot}=\frac{5292}{38.808}=136.36$

As the number of lead shots has to be integral, 136 such lead shots can be obtained.