# Q : 9    Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area $\small S'$. Find the            (i) radius $\small r'$ of the new sphere

H Harsh Kankaria

Given,

The radius of a small sphere = $r$

The radius of the bigger sphere = $r'$

$\therefore$The volume of each small sphere= $\frac{4}{3}\pi r^3$

And, Volume of the big sphere of radius $r'$$\frac{4}{3}\pi r'^3$

According to question,

$27\times\frac{4}{3}\pi r^3=\frac{4}{3}\pi r'^3$

$\\ \Rightarrow r'^3 = 27\times r^3 \\ \Rightarrow r' = 3\times r$

$\therefore r' = 3r$

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