The length of a cold storage is double its breadth. Its height is 3 metres. The area of its four walls (including the doors) is 108 m². Find its volume.

### Concept & Area of Four Walls The area of four walls of a room (lateral surface area) is related to the perimeter of the base and the height. $$\text{Area of 4 walls} = 2(l + b)h$$ ### Step-by-Step Solution * **Given:** Length ($l$) = $2 \times$ breadth ($b$). Height ($h$) = $3 \text{ m}$. Area of 4 walls = $108 \text{ m}^2$. * **Step 1: Set up the equation using variables** Let breadth ($b$) = $x$. Then length ($l$) = $2x$. $2(l + b)h = 108$ $2(2x + x) \times 3 = 108$ * **Step 2: Solve for $x$** $2(3x) \times 3 = 108$ $18x = 108$ $x = \frac{108}{18} = 6$. So, breadth ($b$) = $6 \text{ m}$, and length ($l$) = $12 \text{ m}$. * **Step 3: Calculate the volume** $\text{Volume} = l \times b \times h = 12 \times 6 \times 3$. $\text{Volume} = 72 \times 3 = 216 \text{ m}^3$. ### Exam Strategy & Shortcut Area of walls is Perimeter $\times$ Height. $108 = \text{Perimeter} \times 3 \Rightarrow \text{Perimeter} = 36$. Since $l = 2b$, Perimeter = $2(2b + b) = 6b$. Thus, $6b = 36 \Rightarrow b = 6$. Volume = $2b \times b \times 3 = 6b^2 = 6(36) = 216$. This mental flow requires very little writing. ### Common Pitfall Using the total surface area formula $2(lb + bh + hl)$ instead of just the lateral surface area $2h(l+b)$. The problem explicitly states "area of its four walls". ### Final Answer Therefore, the correct answer is **216 m³**.