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The product of the area of three adjacent faces of a rectangular box 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. Cube root of the volume of the box

Explanation

If the cuboid dimensions are l, b and d, the areas of three adjacent faces are lb, bd and dl. Their product is lb × bd × dl = l2b2d2 = (lbd)2, which is the square of the volume. The likely wrong choice is the volume itself, option a, because students may multiply only one length, breadth and depth instead of all three face areas.

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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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