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The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to :___________?

Correct answer: C. the square of the volume of the box

  • A. the volume of the box
  • B. twice the volume of the box
  • C. the square of the volume of the box
  • D. the cube root of the volume of the box

Explanation

If the box edges are a, b and c, the three adjacent face areas are ab, bc and ca. Their product is ab x bc x ca = a2b2c2 = (abc)2, which is the square of the volume. The likely mistake is option a, caused by confusing the product of face areas with the volume itself.

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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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