Multiple choice

Identical cubes of largest possible size are cut from a solid cuboid of size 65 cm × 26 cm × 39 cm. What is the total surface area (in cm2) of all the small cubes taken together?

  1. 30,420

  2. 15,210

  3. 20,280

  4. 16,440
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A Correct answer
Explanation

The side of the largest cube is the HCF of 65, 26, and 39, which is 13 cm. Number of cubes = (65*26*39) / (13*13*13) = 5 * 2 * 3 = 30 cubes. Surface area of one cube = 6 * 13^2 = 6 * 169 = 1014. Total surface area = 30 * 1014 = 30420.

AI explanation

The side length of the largest possible identical cubes is the highest common factor of 65, 26, and 39, which is 13 cm. The number of cubes formed is the volume of the cuboid divided by the volume of one cube, giving (65 * 26 * 39) / 13^3 = 30 cubes. The total surface area of all the cubes is 30 * 6 * 13^2 = 30 * 6 * 169, resulting in 30420 cm2.

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