A swimming pool, 30 m long has a depth of water of 80 cm at one end and 2.4 m the other end. Find the area of the vertical cross-section of the pool along the length.

Options

A. 54 `m^(2)`
B. 48 `m^(2)`
C. 36 `m^(2)`
D. 42 `m^(2)`

Answer

To find the area of the vertical cross-section of the swimming pool, we can model the cross-section as a trapezium (trapezoid). Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the dimensions of the pool**:
- Length of the pool (L) = 30 m
- Depth at one end (D1) = 80 cm = 0.8 m (convert cm to m)
- Depth at the other end (D2) = 2.4 m

2. **Draw a diagram**:
- Sketch a trapezium where one side (D1) is 0.8 m and the other side (D2) is 2.4 m. The length (L) of the trapezium is 30 m.

3. **Use the formula for the area of a trapezium**:
\[ \text{Area} = \frac{1}{2} \times (D1 + D2) \times L \]

4. **Substitute the values into the formula**:
\[ \text{Area} = \frac{1}{2} \times (0.8 + 2.4) \times 30 \]

5. **Calculate the sum of the depths**:
\[ 0.8 + 2.4 = 3.2 \]

6. **Substitute the sum back into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 3.2 \times 30 \]

7. **Calculate the area**:
- First, calculate \( \frac{1}{2} \times 3.2 = 1.6 \)
- Then, multiply by 30:
\[ 1.6 \times 30 = 48 \text{ m}^2 \]

8. **Final answer**:
The area of the vertical cross-section of the pool is **48 m²**.