Question:
The length of a hall is 22 m and the width is 18 m. If the sum of the areas of the floor and the roof is equal to the total area of the four walls, then what is the volume of the hall?
The length of a hall is 22 m and the width is 18 m. If the sum of the areas of the floor and the roof is equal to the total area of the four walls, then what is the volume of the hall?
Updated On: Sep 16, 2026
- 3850.8 m³
- 3875.5 m³
- 3935.2 m³
- 3920.4 m³
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The Correct Option is D
Solution and Explanation
Concept:
Step 1: Write the floor+roof area and the wall area in terms of height h
Length = 22 m, Breadth = 18 m
Floor + Roof area = 2 x (22 x 18) = 2 x 396 = 792 m²
Total wall area = 2 x h x (22 + 18) = 2 x h x 40 = 80h m²
Step 2: Use the given condition to form an equation and solve for h
792 = 80h
h = 792/80 = 9.9 m
Step 3: Find the volume of the hall
Volume = Length x Breadth x Height = 22 x 18 x 9.9
22 x 18 = 396
396 x 9.9 = 3920.4 m³
Final Answer: 3920.4 m³
- Floor area and roof area of a cuboidal hall are both equal to length x breadth.
- Total area of the 4 walls = 2 x height x (length + breadth).
- Use the given condition to form an equation for height, then apply Volume = length x breadth x height.
Step 1: Write the floor+roof area and the wall area in terms of height h
Length = 22 m, Breadth = 18 m
Floor + Roof area = 2 x (22 x 18) = 2 x 396 = 792 m²
Total wall area = 2 x h x (22 + 18) = 2 x h x 40 = 80h m²
Step 2: Use the given condition to form an equation and solve for h
792 = 80h
h = 792/80 = 9.9 m
Step 3: Find the volume of the hall
Volume = Length x Breadth x Height = 22 x 18 x 9.9
22 x 18 = 396
396 x 9.9 = 3920.4 m³
Final Answer: 3920.4 m³
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