A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter

We have,

Radius of the metallic sphere, $R=\frac{28}{2}=14 \mathrm{~cm}$,

Radius of the smaller cone, $r=\frac{1}{2} \times\left(4 \frac{2}{3}\right)=\frac{1}{2} \times \frac{14}{3}=\frac{7}{3} \mathrm{~cm}$ and

Height of the smaller cone, $h=3 \mathrm{~cm}$

Now,

The number of cones so formed $=\frac{\text { Volume of the metallic sphere }}{\text { Volume of a smaller cone }}$

$=\frac{\left(\frac{4}{3} \pi R^{3}\right)}{\left(\frac{1}{3} \pi r^{2} h\right)}$

$=\frac{4 R^{3}}{r^{2} h}$

$=\frac{4 \times 14 \times 14 \times 14}{\left(\frac{7}{3} \times \frac{7}{3} \times 3\right)}$

$=672$

So, the number of cones so formed is 672.

Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.