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A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Correct answer: C. 25 : 18

  • A. 2 : 1
  • B. 3 : 2
  • C. 25 : 18
  • D. 27 : 20

Explanation

The total surface area of the three small cubes is 6(3 cm)^2 + 6(4 cm)^2 + 6(5 cm)^2 = 54 cm2 + 96 cm2 + 150 cm2 = 300 cm2. Their combined volume is 27 cm3 + 64 cm3 + 125 cm3 = 216 cm3, so the large cube has side 6 cm and surface area 6(6 cm)^2 = 216 cm2. Thus the ratio is 300 cm2 : 216 cm2 = 25 : 18; a likely mistake is comparing volumes instead of surface areas.

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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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