Question : If each edge of a cube is increased by 40%, the percentage increase in its surface area is:
Option 1: 40%
Option 2: 60%
Option 3: 80%
Option 4: 96%
Correct Answer: 96%
Solution :
Given: each side of the cube is increased by 40%
Let the edge of a cube be 100 cm.
New edge after increment of 40% = 140 cm
The surface area of a cube before increment = 6 × 100 × 100 = 60000 cm
2
Surface area of a cube after increment = 6 × 140 × 140 = 117600 cm
2
Percentage increase in surface area = $\frac{\text{Difference}}{\text{Surface area before increment}}×100$
= $\frac{117600-60000}{60000}×100$
= $\frac{57600}{60000}×100$ = 96%
Hence, the correct answer is 96%.
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