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A cuboidal, block of 6 cm X 9 cm X 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be_________?

Correct answer: C. 24

  • A. 6
  • B. 9
  • C. 24
  • D. 30

Explanation

To obtain the least number of equal cubes, use the largest cube edge that divides all three dimensions: gcd(6 cm, 9 cm, 12 cm) = 3 cm. The numbers of cubes along the dimensions are 6/3 = 2, 9/3 = 3 and 12/3 = 4, so total cubes = 2 x 3 x 4 = 24 cubes. The likely mistake is option b, 9 cubes, from dividing by only one dimension or using the wrong cube size.

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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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