Multiple choice

The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which of the following is correct?

  1. 16 < p < 18

  2. 14 < p < 16

  3. 12 < p < 14

  4. 10 < p < 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of a cube = 6 * L^2. If area increases by 25%, new area = 1.25 * 6 * L^2. New length L' = sqrt(1.25) * L = 1.118 * L. The percentage increase p is approximately 11.8%. This falls in the range 10 < p < 12.

AI explanation

Because the surface area of a cube is directly proportional to the square of its side length, we use the formula Final Surface Area / Initial Surface Area = (Final Side / Initial Side)^2. Setting the initial side as 1 gives the initial surface area as 6, and a 25 percent increase makes the new surface area 7.5, so (Final Side)^2 = 7.5 / 6 = 1.25. Taking the square root gives the new side length as approximately 1.118, meaning the percentage increase in length is (0.118 / 1) * 100 = 11.8 percent. The result is 10 < p < 12.

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