The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which one of the following is correct?
- A. 16 \lt p \lt 18
- B. 14 \lt p \lt 16
- C. 12 \lt p \lt 14
- D. 10 \lt p \lt 12 ✓
Correct Answer: D. 10 \lt p \lt 12
Explanation
Surface Area \propto L^2. If area increases by 25\%, the new area is 1.25 times the old. The new length is \sqrt{1.25}L \approx 1.118L. The percentage increase is p \approx 11.8\%. Thus, 10 \lt p \lt 12.
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