Question

a solid sphere of radius 6cm is melted and then recast into small spherical balls each of diameter 0.4 CM. the number of small balls thus obtained is

Answer 1

Volume of sphere = $\frac{4}{3} \pi r^{3}$

Let Radius of small spheres be r and that of big ball be R.

So, Volume of big ball = Volume of small balls

$\frac{4}{3} \pi R^{3}$ = N . $\frac{4}{3} \pi r^{3}$

where N is no. of small balls

So we have,

$\frac{4}{3} \pi (6)^{3} = N . \frac{4}{3} \pi (0.2)^3$

$(6)^3 = N . (0.2)^3$

N = 6³ ÷ (0.2)³

N = 27000