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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 the resulting sphere.
Solution
Radius (r1) of 1st sphere = 6 cm
Radius (r2) of 2nd sphere = 8 cm
Radius (r3) of 3rd sphere = 10 cm
Let the radius of the resulting sphere be r.
The object formed by recasting these spheres will be same in volume as the sum of the volumes of these spheres.
Volume of 3 spheres = Volume of resulting sphere
`4/3pi[r_1^3+r_2^3+r_3^3] = 4/3pir^3`
`4/3pi[6^3+8^3+10^3] = 4/3 pir^3`
r3 = 216 + 512 + 1000 = 1728
r = 12 cm
Therefore, the radius of the sphere so formed will be 12 cm.
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