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?

Explanation

The radii are 3, 4, and 5. The new radius R satisfies R^3 = 3^3+4^3+5^3 = 216 \implies R=6. Initial surface area sum = 4\pi(3^2+4^2+5^2) = 200\pi. New surface area = 4\pi(6^2) = 144\pi. The percentage decrease is \frac{200\pi - 144\pi}{200\pi} \times 100 = 28\%.

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