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# Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the (ii) ratio of S and S′.

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

(ii) ratio of S and $\small S'$.

Views

Given,

The radius of a small sphere = $r$

The surface area of a small sphere = $S$

The radius of the bigger sphere = $r'$

The surface area of the bigger sphere = $S'$

And, $r' = 3r$

We know, the surface area of a sphere =$4\pi r^2$

$\therefore$ The ratio of their surface areas = $\frac{4\pi r'^2}{4\pi r^2}$

$\\ = \frac{ (3r)^2}{ r^2} \\ = 9$

Therefore, the required ratio is $1:9$

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