Each edge of a cube is increased by 12%. By what percentage does its volume increase?

Introduction / Context:Volume scales with the cube of linear dimensions. If each edge increases by 12%, the linear factor is k = 1.12 and the volume factor is k^3. Converting this factor to a percentage increase gives the final answer, illustrating compound scaling in three dimensions.

Given Data / Assumptions:

• Edge factor k = 1.12.
• Volume factor = k^3.

Concept / Approach:Compute k^3 exactly (or to the precision given in options), then subtract 1 and express as a percentage. This reflects multiplicative growth in all three independent directions.

Step-by-Step Solution:k^2 = 1.12^2 = 1.2544k^3 = 1.2544 * 1.12 = 1.404928Percentage increase = (1.404928 − 1) * 100% = 40.4928%

Verification / Alternative check:Small-increase approximation 3 * 12% = 36% underestimates because it ignores compounding; the exact is 40.4928%, as computed.

Why Other Options Are Wrong:50.5240% and 60.3292% are too large; 30.4928% is too small and confuses squared with cubed growth.

Common Pitfalls:Tripling 12% without compounding; rounding mid-calculation; mixing area and volume scaling.

Final Answer:40.4928%