Multiple choice

A cube of white chalk is painted red and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids in not painted red?

  1. $45$%
  2. $25$%
  3. $40$%
  4. $50$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cutting the painted cube into two equal cuboids exposes one new square face on each solid. Each cuboid has total surface area 4s^2, while the unpainted face has area s^2, giving 1/4 or 25%.

AI explanation

Let the original cube have an edge length of 2x, making its total surface area 6 * (2x)^2 = 24x^2. Cutting it in half creates two rectangular solids with dimensions 2x by 2x by x, and the surface area of one solid is 2*(2x*2x) + 4*(2x*x) = 16x^2. The cut creates two new unpainted faces of area 2x * 2x = 4x^2 each. The percentage of the surface area not painted red is (4x^2 / 16x^2) * 100, which equals 25%.

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