Question : If each side of a cube is decreased by 12%, then the percentage decrease in its surface area is:
Option 1: 25.66%
Option 2: 28.23%
Option 3: 22.56%
Option 4: 26.54%
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Correct Answer: 22.56%
Solution : Let the side of the cube be 10 units. Surface area of cube, $S_1$ = 6(side) 2 = 6(10) 2 Side of cube after 12% decrease in size = 10 – 12% of 10 = 8.8 units New surface area of cube, $S_2$ = 6(side) 2 = 6(8.8) 2 The percentage decrease in its surface area = $\frac{S_1-S_2}{S_1}\times 100$ = $\frac{6(10)^2-6(8.8)^2}{6(10)^2}\times 100$ = 10 2 – 8.8 2 = 22.56% Hence, the correct answer is 22.56%.
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