Question

A hall is \(15\ \text{m}\) long and \(12\ \text{m}\) broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

• A. \(720\)
• B. \(900\)
• C. \(1200\)
• D. \(2000\)

Hint:

In hall problems, the area of four walls = perimeter of base × height. Equating given areas can directly yield the height before finding volume.

Answer 1

The Correct Option is C

Step 1 (Let height be \(h\)).
Length \(l = 15\ \text{m}\), breadth \(b = 12\ \text{m}\).
Area of floor = \(l \times b = 15 \times 12 = 180\ \text{m}^2\).
Area of ceiling = same as floor = \(180\ \text{m}^2\).
Sum of floor and ceiling areas = \(180 + 180 = 360\ \text{m}^2\).
Step 2 (Area of four walls).
Area of four walls = Perimeter of base \(\times\) height = \(2(l + b) \times h\) = \(2(15 + 1(b)h = 54h\ \text{m}^2\).
Step 3 (Equating areas as given).
\[ 360 = 54h \ \ h = \frac{360}{54} = 6.666\ \text{m} = \frac{20}{3}\ \text{m} \] Step 4 (Volume of the hall).
Volume = \(l \times b \times h = 15 \times 12 \times \frac{20}{3} = 15 \times 4 \times 20 = 1200\ \text{m}^3\).
\[ \boxed{1200\ \text{m}^3 \ \text{(Option (c)}} \]