Cube side reduced — percent decrease in surface area: If each side of a cube is decreased by 19%, find the percentage decrease in its total surface area.

Introduction / Context:
Total surface area of a cube is proportional to a^2 (since TSA = 6a^2). Reducing the side by p% reduces area by the square of the side factor.

Given Data / Assumptions:
a_new = 0.81 a (19% decrease).

Concept / Approach:
Area factor = (0.81)^2; percent decrease = (1 − factor) * 100%.

Step-by-Step Solution:
(0.81)^2 = 0.6561Decrease = (1 − 0.6561)*100% = 34.39%

Verification / Alternative check:
Matches the rule: for small p, area decreases by approximately 2p (here ~38%), but exact is 34.39% because 19% is not very small.

Why Other Options Are Wrong:
40.4% and 38.4% overestimate by linear approximation; 35.6% is still off.

Common Pitfalls:
Using 2 * 19% exactly instead of squaring the factor.

Final Answer:
34.39%