A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling equals the sum of the areas of the four walls, what is the volume of the hall?

Problem Restatement

Use the relation between floor/ceiling areas and wall areas to determine the height, then compute volume.

Given data

• Length L = 15 m
• Breadth B = 12 m
• Unknown height = H

Concept / Relations

• Floor area = Ceiling area = L × B
• Sum of floor and ceiling = 2LB
• Area of four walls = 2H(L + B)

Step-by-step calculation

Given: 2LB = 2H(L + B)2(15)(12) = 2H(27) → 360 = 54H → H = 360 ÷ 54 = 20/3 mVolume = L × B × H = 15 × 12 × (20/3) = 1200 m^3

Final Answer

Volume of the hall = 1200 m^3.