Question

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively, are melted to form a
single solid sphere. Find the radius of resulting sphere.
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Answer 1

Let the radii of these 3 spheres be r1, r2 and r3 as 6, 8 and 10 cm respectively and radius of resulting sphere be R cm.

A.T.Q

Volume of resulting sphere = Volume of all three sphere

4/3πR^3 = 4/3πr1^3 + 4/3πr2^3 + 4/3πr3^3

4/3πR^3 = 4/3π(r1^3 + r2^3 + r3^3)

4/3π cancelled from both sides..

R^3 = (6^3 + 8^3 + 10^3)

R^3 = (216 + 512 + 1000)

R^3 = 1728

R = 12 cm

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