Question

If r₁ and r₂ be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is$(r_{1}^{3} +r _{2}^{3}) .^{\frac{1}{3}}$

Answer 1

SOLUTION :  

Given :  

r1 and r2 be the radius of a two solid metallic spheres.

Let r3  be the radius of new sphere.

Volume of first sphere, V1 = 4/3 πr1³

Volume of second sphere, V2 = 4/3 πr2³

Here, two solid metallic spheres are melted and converted into one solid sphere.

Volume of new sphere, V = Volume of first sphere + Volume of second sphere

V = V1 + V2

4/3 πr3³ = 4/3 πr1³ + 4/3 πr2³

4/3 πr3³ = 4/3 π (r1³ + r2³)

r3³ = (r1³ + r2³)

r3 = (r1³ + r2³)^⅓

Radius of new sphere = (r1³ + r2³)^⅓

Hence proved..

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Answer 2

The solution is provided in the attachment .

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