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The edges of a cuboid are in the ratio 1 : 2 : 3 and its sunface area is 88 cm2. The volume of the cuboid is :_________?

Correct answer: B. 48 cm3

  • A. 24 cm3
  • B. 48 cm3
  • C. 64 cm3
  • D. 120 cm3

Explanation

Let the edges be x cm, 2x cm and 3x cm. The total surface area is 2(x x 2x + 2x x 3x + 3x x x) = 22x2 cm2, so 22x2 cm2 = 88 cm2 gives x = 2 cm. Therefore, volume = 2 cm x 4 cm x 6 cm = 48 cm3. The likely mistake is option a, 24 cm3, from using half the total surface area or an incorrect scale factor.

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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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