2018 · Q86
A cube of maximum volume (each corner touching the surface from inside) is cut from a sphere. What is the ratio of the volume of the cube to that of the sphere?
Elementary MathematicsMensuration
- A3:4π
- B√3:2π
- C2:√3π
- D4:3π
Explanation
The inscribed cube's space diagonal equals the sphere's diameter: s√3 = 2R, so s = 2R/√3. Volume ratio = (8R³/(3√3)) / ((4/3)πR³) = 2/(√3π), i.e. 2 : √3π, option (C).