 # How many spherical lead shots each having diameter 3 cm `
Question:

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

Solution:

Given a cuboidal lead solid with dimensions 9 cm × 11 cm × 12 cm

We have to find the number of spherical lead shots each having a diameter

Let the length of cuboidal lead solid L = 9 cm

Let the length of cuboidal lead solid H = 9 cm

Let the number of spherical lead shots = x

Volume of a spherical lead shot $=\frac{4}{3} \pi r^{3}$

Radius of a spherical lead shot $=\frac{1}{2} \times$ diameter

$=\frac{1}{2} \times 3$

$=\frac{3}{2}$

Volume of the cuboidal lead solid $=L \times B \times H$

$=9 \mathrm{~cm} \times 11 \mathrm{~cm} \times 12 \mathrm{~cm}$

Volume of the cubical lead shot $=\frac{4}{3} \times \frac{22}{7} \times\left(\frac{3}{2}\right)^{3}$

Therefore the number of spherical lead shots $x=\frac{9 \times 11 \times 12}{\frac{4}{3} \times \frac{22}{7} \times\left(\frac{3}{2}\right)^{3}}$

$=84$