Three solid lead spheres of diameters 6 cm, 8 cm and 10 cm are melted together and recast as a solid sphere. What is the percentage diminution of the surface area as compared to the sum of the surface areas of the three spheres?
A.27%
B.25%
C.26%
D.28%✓ Correct
Explanation
Volumes: (4π/3)(27+64+125) = (4π/3)·216. New radius: r³ = 216, r = 6. New surface = 4π·36 = 144π. Old surfaces sum = 4π(9+16+25) = 4π·50 = 200π. Diminution = (200−144)/200 = 56/200 = 28%.
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