Find the ratio of the surface area of a cube to that of... – Mensuration

Mensurationhard · Past Paper

Find the ratio of the surface area of a cube to that of a sphere of the same volume.

A∛(6/π) : 1

B1 : 1

C6 : π

D√(6/π) : 1

✓ Correct Answer: A — ∛(6/π) : 1

Let vol V. Cube side a=V^(1/3). Area = 6V^(2/3). Sphere radius r=(3V/4π)^(1/3). Area = 4π(3V/4π)^(2/3). Ratio simplifies to (6/π)^(1/3) : 1.

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