The volume of a rectangular pool is `182m^(3)`. If its length and breadth be 8 m abd 6.5 m respectivley. Find its depth.

Options

A. `2.5` cm
B. `4.5` cm
C. `3.5` cm
D. `5.5` cm

Answer

To find the depth of the rectangular pool, we can follow these steps:

### Step 1: Write down the formula for the volume of a rectangular prism.
The volume \( V \) of a rectangular prism (or pool in this case) is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{depth} \]

### Step 2: Substitute the known values into the formula.
We know the volume \( V = 182 \, m^3 \), length \( L = 8 \, m \), and breadth \( B = 6.5 \, m \). Plugging these values into the formula gives:
\[ 182 = 8 \times 6.5 \times \text{depth} \]

### Step 3: Calculate the product of length and breadth.
First, calculate \( 8 \times 6.5 \):
\[ 8 \times 6.5 = 52 \]
Now we can rewrite the equation:
\[ 182 = 52 \times \text{depth} \]

### Step 4: Solve for depth.
To find the depth, we need to isolate it on one side of the equation. We do this by dividing both sides by 52:
\[ \text{depth} = \frac{182}{52} \]

### Step 5: Simplify the fraction.
Now, we can simplify \( \frac{182}{52} \). Both numbers can be divided by 26:
\[ \frac{182 \div 26}{52 \div 26} = \frac{7}{2} \]
Thus, we have:
\[ \text{depth} = 3.5 \, m \]

### Conclusion:
Therefore, the depth of the rectangular pool is:
\[ \text{depth} = 3.5 \, m \]

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