2026 · Q73
A cubical wooden block of length 10 cm is sliced to produce a cross-section of maximum area. What is the area of the cross-section?
Elementary MathematicsMensuration
- A100 cm²
- B100√2 cm²
- C100√3 cm²
- D200 cm²
Explanation
A plane section of a cube has maximum area when it passes through a pair of opposite edges, giving a rectangle of sides 10 and the face diagonal 10√2. Its area is 10 × 10√2 = 100√2 cm², option B. (The regular-hexagon central section has area 75√3 ≈ 129.9 < 141.4, so it is not maximal.)