2021 · Q30
The surface area of a cube is equal to that of a sphere. If x is the volume of the cube and y is the volume of the sphere, then what is x² : y² equal to?
Elementary MathematicsMensuration
- Aπ : 6
- B6 : π
- Cπ : 3
- D3 : π
Explanation
From 6a² = 4πR² we get a² = 2πR²/3. Then x²/y² = a⁶/[(16/9)π²R⁶] = (a²/R²)³·9/(16π²) = (2π/3)³·9/(16π²) = π/6. Hence option A.