Question

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter $4\frac{2}{3}$ cm and height 3 cm. Find the number of cones so formed.

Answer 1

We have,

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

Radius of the smaller cone,
r = $\frac{1}{2}\times \frac{14}{3}$ = $\frac{7}{3}$ cm and

Height of the smaller cone, h = 3 cm

Now,

The number of cones so formed = Volume of the metallic sphere / Volume of a smaller cone

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

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

= $\frac{4\times 14\times 14\times 14}{\frac{7}{3}\times \frac{7}{3}\times 3}$
= 672

So, the number of cones so formed is 672.