The length, breadth and height of a cuboid are in the ratio 27:8:1. The cuboid is melted and recast into a cube. If p is the surface area of the cuboid and q is the surface area of the cube, then what is p/q equal to?

Explanation

Let dimensions be 27k, 8k, k. Volume = 216k^3. The side of the new cube a = \sqrt{216k^3} = 6k. Cuboid surface area p = 2(27\times8 + 8\times1 + 27\times1)k^2 = 2(216 + 8 + 27)k^2 = 502k^2. Cube surface area q = 6a^2 = 6(36k^2) = 216k^2. The ratio is \frac{p}{q} = \frac{502}{216} = \frac{251}{108}.

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