Course / Category - 10th

Concept Detail
Maths / Surface Area and Volume / Melting and Recasting
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## Melting and Recasting

Conversion From One Shape to Another: When you convert one solid shape to another, its volume remains the same, no matter how different the new shape is.

Example: 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:   $\dpi{100} \large (i)$  radius r' of the new sphere. $\dpi{100} \large (ii)$ ratio of S and S'

Solution:  $\dpi{100} \large (i)$  We have, Volume of 27 solid spheres, each of radius r =$\dpi{100} \large 27\times \frac{4}{3}\pi r^{3} = 36 \pi r^{3}$

But volume of 27 solid spheres = Volume of sphere of radius r1 $\fn_jvn \large 36 \pi r^{3} = \frac{4}{3}\pi r_1^{3} \Rightarrow r_1^{3} \Rightarrow r_1 = 3r$

$\dpi{120} \large (ii)$ We have,  $\dpi{120} \large S_1 = 4\pi r_1^{2} = 4\pi \times (3r)^{2} = 36\pi r^{2}$

$\dpi{120} \large \therefore$          $\dpi{120} \large S:S1=4\pi r^{2} : 36\pi r^{2} = 1:9$

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