Q11 of 67 Page 195

Three solid sphere of iron whose radii are 6 cm, 8 cm and 10 cm respectively are melted into a single solid sphere. Find the radius of the solid sphere.

Three spheres are melted and one big sphere is made out of the melted spheres


Thus volume of sphere formed will be same as volume of 3 melted spheres


Let the radius of spheres be r1 = 6 cm, r2 = 8 cm and r3 = 10 cm


⇒ Volume of spheres melted = πr13 + πr23 + πr33


= π(r13 + r23 + r33)


Let r be the radius of sphere formed


⇒ Volume of sphere formed = πr3


As volumes are same


⇒ Volume of spheres melted = Volume of sphere formed


⇒ π(r13 + r23 + r33) = πr3


⇒ r13 + r23 + r33 = r3


Substituting values


⇒ 63 + 83 + 103 = r3


⇒ 216 + 512 + 1000 = r3


⇒ r3 = 1728


⇒ r = 12 cm


Therefore, radius of sphere made is 12 cm


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