A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and breadth of the reservoir is 3.5 m, then the depth of the reservoir will be (R.R.B., 2006)

### Concept & Finding Missing Dimension from Volume When capacity in litres is given, convert it to cubic meters to match the linear dimensions, then use the volume formula to solve for the missing dimension (depth). $$\text{Volume} (m^3) = \frac{\text{Capacity in Litres}}{1000}$$ $$\text{Volume} = l \times b \times h$$ ### Step-by-Step Solution * **Given:** Capacity = $42,000\text{ litres}$, Length ($l$) = $6\text{ m}$, Breadth ($b$) = $3.5\text{ m}$. * **Step 1: Convert Litres to Cubic Meters** $\text{Volume} = \frac{42000}{1000} = 42\text{ m}^3$. * **Step 2: Set up the volume equation** $42 = l \times b \times h$ $42 = 6 \times 3.5 \times h$ * **Step 3: Solve for $h$ (depth)** $6 \times 3.5 = 21$ $42 = 21 \times h$ $h = \frac{42}{21} = 2\text{ m}$. ### Exam Strategy & Shortcut Work with the numbers efficiently. $3.5 \times 6$ is the same as $7 \times 3 = 21$. You know the volume is 42 (dropping the zeroes due to litre to $m^3$ conversion). Mentally calculate $\frac{42}{21} = 2$. ### Common Pitfall Failing to convert litres to cubic meters properly. If someone uses 42000 directly in the formula, they will get a ridiculously large number for the depth. ### Final Answer Therefore, the correct answer is **2 m**.