If the side of a cube is increased by 100%, then by what percentage is the surface area of the cube increased?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 300%
The surface area of a cube is \(6a^{2}\), so it grows with the square of the side. Increasing the side by 100% doubles it.
Original surface area \(=6a^{2}\)
New side \(=2a\), so new surface area \(=6(2a)^{2}=24a^{2}\), four times the original
Increase \(\displaystyle =\frac{24a^{2}-6a^{2}}{6a^{2}}\times100=300\%\)
Tip: The area becomes 4 times, but the increase is 3 times the original, that is, 300%; 400% is the new area as a percentage of the old.