Cube volume from space diagonal: The space diagonal of a cube is (14 × √3) cm. Find the volume of the cube (in cm3).

Introduction / Context:Again we relate a cube’s space diagonal to its edge and then compute the volume. This is a direct geometry formula application.

Given Data / Assumptions:

• Space diagonal d = 14√3 cm
• For a cube: d = a√3, volume V = a^3

Concept / Approach:

• Solve for edge a, then compute V = a^3.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 2744√3 cm3: Incorrectly carries the √3 into volume.
• 588 cm3, 3528 cm3: Not equal to a^3 for any integer a here.

Common Pitfalls:

• Mistaking face diagonal (a√2) for space diagonal (a√3).
• Forgetting to cube the edge length.

Final Answer:

2744 cm3