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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