2026 · Q66
A thin metallic sheet, 1.92 m² in area, is cut into two equal pieces. One piece is used to make a hollow cube of volume P (in m³) and the other is used to make a hollow cuboid of volume Q (in m³) with dimensions in the ratio 4 : 2 : 1. If no sheet is wasted, which one of the following is correct?
Elementary MathematicsMensuration
- A343Q² = 216P²
- B343Q² = 225P²
- C49Q² = 64P²
- D49Q² = 25P²
Explanation
Each piece has area 0.96 m². For the cube, 6a² = 0.96 gives a = 0.4 m, so P = 0.064 m³. For the cuboid with sides 4t, 2t, t, the surface area 2(8t² + 2t² + 4t²) = 28t² = 0.96 and volume Q = 8t³. Then 343Q² = 343·64t⁶ = 21952t⁶ = 21952·(0.96/28)³ = 21952·0.884736/21952 = 0.884736, while 216P² = 216·0.004096 = 0.884736. Hence 343Q² = 216P², option A.