A swimming pool is 18m long and 8m wide. Its deep and shallow ends are 2m and 1.2m respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly.

Answer

To find the capacity of the swimming pool, we will follow these steps:

### Step 1: Identify the dimensions of the pool
- Length of the pool (L) = 18 meters
- Width of the pool (W) = 8 meters
- Depth at the shallow end (D1) = 1.2 meters
- Depth at the deep end (D2) = 2.0 meters

### Step 2: Calculate the average depth of the pool
Since the bottom of the pool slopes uniformly from the shallow end to the deep end, we can find the average depth (D_avg) by taking the average of the two depths:
\[ D_{avg} = \frac{D1 + D2}{2} = \frac{1.2 + 2.0}{2} = \frac{3.2}{2} = 1.6 \text{ meters} \]

### Step 3: Calculate the volume of the pool
The volume (V) of the pool can be calculated using the formula for the volume of a rectangular prism (cuboid):
\[ V = L \times W \times D_{avg} \]
Substituting the values we have:
\[ V = 18 \times 8 \times 1.6 \]

### Step 4: Perform the multiplication
Calculating the volume:
\[ V = 18 \times 8 = 144 \]
Now, multiply this result by the average depth:
\[ V = 144 \times 1.6 = 230.4 \text{ cubic meters} \]

### Conclusion
The capacity of the swimming pool is **230.4 cubic meters**.

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