Question

A solid sphere of radius 3 cm is melted and then cast into small balls each of radius 0.3 cm find the number of ball thus obtained

Answer 1

It is volume of big sphere by small sphere;
=>(4/3*3.14*3^3)/(4/3*3.14*0.3^3).
=>27/0.027=1000.
Therefore 1000 balls can be made.

Answer 2

AnswEr :

$\:\bullet\:\sf\ Radius \: of \: sphere = 3cm$

$\:\bullet\:\sf\ Radius \: of \: ball = 0.3cm$

$\:\bullet\:\sf\ Total \: number \: of \: balls =?$

$\rule{100}1$

Let me told you to how solve your question. First of all, sphere is melted to form small balls (we don't the know the number of balls, so let them "n" ).Also, Volume of sphere = Volume of balls.

$\rule{100}2$

$\underline{\dag\:\textsf{Let's \: head \: to \: the \: question \: now:}}$

$\normalsize\star{\boxed{\sf{ Volume \: of \: sphere(\frac{2}{3} \pi R^3) = Volume \: of \: balls(\frac{2}{3} \pi r^3)}}}$

$\normalsize\ : \implies\sf\frac{2}{3} \times\ \pi \times\ (3)^3 = n \times\ \frac{2}{3} \times\ \pi \times\ (0.3)^3 \\ \\ \normalsize\ : \implies\sf\ n = \frac{\cancel{\frac{2}{3}} \times\ \cancel{\pi} \times\ (3)^3}{\cancel{\frac{2}{3}}\times\ \cancel{\pi} \times\ (0.3)^3} \\ \\ \normalsize\ : \implies\sf\ n = \frac{ 3 \times\ 3 \times\ 3}{0.3 \times\ 0.3 \times\ 0.3} \\ \\ \normalsize\ : \implies\sf\ n = \frac{27}{0.027} \\ \\ \normalsize\ : \implies\sf\ n = \frac{\cancel{27}}{\cancel{0027}} \times\ \frac{1000}{1} \\ \\ \normalsize\ : \implies\sf\ n = 1000$

$\therefore\underline{\textsf{ Hence, \: the \: total \: number \: of \: balls \; are \: \blue{1000} }}$