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Two solid hemispheres of radii 3 cm and 5 cm are melted together and recast into a single hemisphere. Find the approximate total surface area of the new hemisphere.

1. 245 cm^2
2. 280 cm^2
3. 268 cm^2
4. 292 cm^2

Correct answer: 268 cm^2

Solution

Equating volumes, r^3 = 3^3 + 5^3 = 152, so r is about 5.34 cm. Total surface area of a hemisphere = 3*pi*r^2 = 3*3.14*28.5, roughly 268 cm^2.

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