Diagonal of a cube from side length: A cube has side 9 cm. Find the length of its space diagonal (in cm).

Introduction / Context:The space diagonal in a cube is a standard formula application: d = s√3. This checks quick recall and substitution without overthinking.

Given Data / Assumptions:

• s = 9 cm
• d = s√3

Concept / Approach:Apply the space diagonal formula for cubes.

Step-by-Step Solution:d = 9√3 cm

Verification / Alternative check:3D Pythagoras from two orthogonal face diagonals also yields s√3, reinforcing correctness.

Why Other Options Are Wrong:Other multiples of √3 correspond to different side lengths; only 9√3 matches s = 9 cm.

Common Pitfalls:Confusing face diagonal (s√2) with space diagonal (s√3).

Final Answer:9√3