Multiple choice

Side of a cube is increased by 50%. What will be the percent increase in the area of the vertical faces of the cube?

  1. 125%

  2. 150%

  3. 100%

  4. 50%
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A Correct answer
Explanation

Area of vertical faces of a cube is 4s^2. If side s increases by 50%, new side is 1.5s. New area = 4*(1.5s)^2 = 4*2.25s^2 = 9s^2. Increase = (9s^2 - 4s^2) / 4s^2 = 5/4 = 125%.

AI explanation

The area of a face of the cube is proportional to the square of its side length. If the side is increased by 50%, the new side is 1.5 times the original, so the new area is 1.5 squared, or 2.25 times the original area. Since the new area is 225% of the original area, this represents a 125% increase in the area of the vertical faces.

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