Question

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.

Answer 1

The length of the edge of the cube be x = 44 cm

Volume of the cube $=x^3={44}^3=85184c{m}^3$

Diameter of spherical lead = 4 cm
Thus, radius of the spherical spherical lead, r = 42 = 2 cm

volume of the one spherical lead $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 2^3=\frac{32\times 22}{21}c{m}^3$

Let n number of spherical lead can be made.

Therefore, the volume of n spherical lead = volume of the cube

$n\times \frac{32\times 22}{21}=85184$

$n=\frac{85184\times 21}{32\times 22}=2541$

Thus 2541 lead can be made.