Correct Answer: D
Explanation:
Let the radius of the sphere so formed be r cm.
Given –
Radius of 1st sphere(r1) = 6 cm
Radius of 2nd sphere(r2) = 8 cm
Radius of 3rd sphere(r3) = 10 cm
After Melting all these spheres, the volume will remain unchaged.
∴ Vol. of 1st sphere + Vol. of 2nd sphere + Vol. of 3rd sphere
= Vol. of new sphere so formed
⇒ (4/3)π(r1)3 + (4/3)π(r2)3 + (4/3)π(r3)3 = (4/3)π(r)3
Taking out (4/3)π from both sides, we get –
⇒ (r1)3 + (r2)3 + (r3)3 = (r)3
⇒ (6)3+ (8)3 + (10)3 = (r)3
⇒ 216 + 512 + 1000 = (r)3
⇒ (r)3 = 1728
∴ r = 12 cm
Thus, the radius of new sphere is 12 cm.