If every edge of a cube is increased by 25%, what is the percentage increase in its surface area?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 56.25%
The surface area of a cube is \(6a^2\), so it changes as the square of the edge: the edge factor is applied twice.
New edge \(=1.25a\)
New surface area \(=6(1.25a)^2=1.5625\times6a^2\)
Increase \(=(1.5625-1)\times100=56.25\%\)
Why the other options are incorrect
Option (2) 25% — Incorrect. This is the increase in the edge only; area depends on the edge squared.
Option (3) 50% — Incorrect. This just doubles 25% and leaves out the extra \(25\%\times25\%=6.25\%\).
Option (4) No change — Incorrect. Every face grows when the edge grows, so the surface area must increase.