Multiple choice

A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given cube and that of one of the cuboids.

  1. $3:2$
  2. $2:1$
  3. $1:2$
  4. $2:3$
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A Correct answer
Explanation

Cube side s, surface area 6s^2. Cut into two equal cuboids, each has dimensions s by s by s/2. Surface area of one cuboid = 2(s*s + s*s/2 + s*s/2) = 2(s^2 + s^2/2 + s^2/2) = 2(2s^2) = 4s^2. Ratio 6s^2 : 4s^2 = 3:2.

AI explanation

Assuming the original cube has a side length of s, its total surface area is 6s^2. Cutting the cube into two equal cuboids creates rectangular solids with dimensions s by s by s/2, giving one cuboid a total surface area of 2(s * s) + 4(s * s/2), which equals 4s^2. The ratio of the surface area of the original cube to one cuboid is 6s^2 : 4s^2, simplifying to 3:2.

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