How many spherical lead shots each having a diameter of 3 cm can be made from a cuboidal lead solid of dimensions 9 cm x 11 cm x 12 cm ?

We are given a cuboidal lead solid, which is then converted into spherical lead shots, and we must determine the number of shots that can be made. We need the formula for the volume of the cuboid and the volume of the sphere to find the required answer.

We know that, Volume of a cuboid $=\mathrm{lbh}=9\times 11\times 12=1188{ \mathrm{cm}}^3$

Given : Diameter of lead shot $=3 \mathrm{cm}$ 

Radius of lead shot $=1.5 \mathrm{cm}$

Volume of one lead shot $=4/3\pi {\text{r}}^3$

$=4/3\times 22/7\times 1.5\times 1.5\times 1.5$

$=14.14 {\text{cm}}^3$

Number of lead shots = Volume of cuboid/Volume of one lead shot

$=1188/14.14\approx 84$ shots