Question

An iron right circular cone of diameter $8cm$ and height $12cm$ is melted and recast into spherical lead shots each of radius $4mm$. How many lead shots can be made?

Answer 1

We have,

$d=8cm$

$r=4cm$

$h=12cm$

We know that the volume of the cone

$=\frac{1}{3}\pi r^{2}h$

So,

$=\frac{1}{3}\pi \times 4^2\times 12$

$=\pi \times 4^{3}c{m}^3$

Since, this cone is melted and recast into a spherical lead which radius is $4mm$

Let the number of lead shots be $x$.

So,

$x\times \frac{4}{3}\pi \times (4mm{)}^3=\pi \times 4^{3}c{m}^3$

$x\times \frac{4}{3}\times 4^3\times (0.1cm{)}^3=4^{3}c{m}^3$

$x\times \frac{4}{3}\times {10}^{-3}=1$

$x\times \frac{4}{3}=1000$

$x=1000\times \frac{3}{4}=750$

Hence, this is the answer.