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:   large (i)  radius r' of the new sphere. large (ii) ratio of S and S'

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

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

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

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

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