Multiple choice

A solid cube of volume 13,824 cm3 is cut into 8 cubes of equal volumes. The ratio of the surface area of the original cube to the sum of the surface areas of three of the smaller cubes is:

  1. 2 : 3

  2. 4 : 3

  3. 8 : 3

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original volume = 13824, side = 24. Surface area = 6 * 24^2 = 3456. 8 smaller cubes, volume = 13824 / 8 = 1728. Side of small cube = 12. Surface area of one small cube = 6 * 12^2 = 864. Sum of surface areas of 3 small cubes = 3 * 864 = 2592. Ratio = 3456 / 2592 = 4 / 3.

AI explanation

When a solid cube is cut into 8 smaller cubes of equal volume, the side length of each small cube is half that of the original cube. Since surface area is proportional to the square of the side length, each small cube has a surface area equal to 1/4 of the original cube. Therefore, the ratio of the surface area of the original cube to the sum of the surface areas of three smaller cubes is 1 to (3 * 1/4), which simplifies to 4 : 3.

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