Two cubes have volumes in the ratio 8 : 1. Find the ratio of their edges.

Introduction / Context:
For similar solids (including cubes), volume scales as the cube of the linear dimension. If V1 : V2 = 8 : 1, then (a1/a2)^3 = 8/1, so the edge-length ratio is the cube root of the volume ratio.

Given Data / Assumptions:

• V1 : V2 = 8 : 1.
• V ∝ a^3 for cubes.

Concept / Approach:
Take cube roots of both sides of the ratio: (a1/a2) = ∛(8/1) = 2/1.

Step-by-Step Solution:
(a1/a2)^3 = 8 ⇒ a1/a2 = 2

Verification / Alternative check:
Let a2 = 1 ⇒ V2 = 1; set a1 = 2 ⇒ V1 = 8; ratio holds.

Why Other Options Are Wrong:
8 : 1 is a volume ratio; 2√2 : 1 is irrelevant; “None” is unnecessary because 2 : 1 is correct.

Common Pitfalls:
Squaring or leaving the ratio unchanged instead of taking cube roots.

Final Answer:
2 : 1