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The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?

Correct answer: C. 9:25

  • A. 6:25
  • B. 3:5
  • C. 9:25
  • D. 16:25

Explanation

Cube volume is proportional to the cube of its edge, so a volume ratio of 27:125 gives an edge ratio of 3:5. Surface area is proportional to the square of the edge, giving 3²:5² = 9:25. The likely wrong choice is 3:5, which is the edge ratio, not the surface-area ratio.

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About Area and Volume

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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