2026 · Q47
Let x be the length of a diagonal of a face of a cube and y be the length of a diagonal of the cube. If x + y = (5 + 2√6) units, then what is the total surface area of the cube?
Elementary MathematicsMensuration
- A6(x + y)
- B6xy
- C3(x + y)
- D3xy
Explanation
With cube side s, the face diagonal is x=s√2 and the space diagonal y=s√3. Then x+y=(√2+√3)s=5+2√6=(√2+√3)², so s=√2+√3. The total surface area 6s²=6(5+2√6)=6(x+y), option A.