If every edge of a cube is increased by 20%, what is the percentage increase in its surface area?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 44%
Surface area \(=6a^2\) depends on the square of the edge, so the factor for the edge is squared.
New edge \(=1.2a\)
New surface area \(=6(1.2a)^2=1.44\times6a^2\)
Increase \(=1.44-1=0.44\), that is 44%
Why the other options are incorrect
Option (1) 20% — Incorrect. This is the change in the edge; the area grows by the square of the factor.
Option (2) 40% — Incorrect. This doubles 20%, forgetting the extra \(0.2\times0.2=0.04\).
Option (4) 72.8% — Incorrect. This is the change in the volume, \(1.2^3=1.728\).