Q31 of 34 Page 1

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

r1 = 6 cm


r2 = 8 cm


r3 = 10 cm


Volume of sphere = 4/3 π r3


Volume of the resulting sphere = Sum of the volumes of the smaller spheres.


4/3 π r3 = 4/3 π r 13 + 4/3 π r23 + 4/3 π r33


4/3 π r3 = 4/3 π (r 13 + r23 + r33)


r3 = 63 + 83 + 103


r3 = 1728


r = √17283


r = 12 cm


Therefore, the radius of the resulting sphere is 12cm.


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