If each side of a cube is reduced by 50%, the surface area will be reduced by
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 75%
The surface area of a cube is \(6a^2\), so it changes as the square of the side. Halving the side makes the area one quarter of what it was.
New side \(\displaystyle =\frac{a}{2}\)
New surface area \(\displaystyle =6\left(\frac{a}{2}\right)^2=\frac{6a^2}{4}\), one quarter of the old area
Reduction \(\displaystyle =1-\frac{1}{4}=\frac{3}{4}\), that is, 75%
Tip: Lengths scale by \(k\), areas by \(k^2\) and volumes by \(k^3\). With \(k=\frac{1}{2}\), the area falls to \(\frac{1}{4}\) and the volume to \(\frac{1}{8}\), so a 50% cut in the side never means a 50% cut in the area.