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A hall is a 15m long and 12m board. If the sum of the areas of the floor and the ceiling is equal to the areas of the 4 walls the volume of the hall is:

Correct answer: B. 1200 Cu.m

  • A. 720 Cu.m
  • B. 1200 Cu.m
  • C. 361 Sq.cm
  • D. None of these

Explanation

Let the height be h m. The floor and ceiling area is 2(15 m × 12 m) = 360 m2, while the four walls have area 2h(15 m + 12 m) = 54h m2, so h = 360 m2 ÷ 54 m = 20/3 m. Therefore volume = 15 m × 12 m × 20/3 m = 1200 m3. The likely wrong choice is 720 m3, caused by using an incorrect height or confusing area with volume.

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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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