2026 · Q69
The volume of a cube is 8 cm³ and is equal to the volume of a cuboid of length x, breadth y and height z, where x, y and z are natural numbers (x > y > z). Let n be the number of such cuboids with different dimensions. What is the value of n?
Elementary MathematicsNumber System
- A1
- B2
- C3
- DMore than 3
Explanation
We need xyz=8 with x>y>z natural numbers. The factorisations 8·1·1 and 2·2·2 violate the strict inequalities; only 4×2×1 works, so n=1, option A. Order matters only through x>y>z, and 4>2>1 is the unique strictly decreasing triple of natural factors.