A swimming pool, 30 m long has a depth of water 0.80 m at one end and 2.4 m at the other end. The area of the vertical cross-section of the pool along the length is :

Question

Accepted Answer

To determine the area of the vertical cross-section of the swimming pool along its length, we need to consider the shape of the cross-section. The pool has a trapezoidal cross-section because one end is deeper than the other.

The formula for the area of a trapezoid is:

$$ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} $$

In this scenario:
- $\text{Base}_1$ is the depth of the water at the shallow end, which is 0.80 m.
- $\text{Base}_2$ is the depth of the water at the deep end, which is 2.4 m.
- $\text{Height}$ is the length of the pool, which is 30 m.

Plugging these values into the formula gives:

$$ \text{Area} = \frac{1}{2} \times (0.80 + 2.4) \times 30 $$

$$ \text{Area} = \frac{1}{2} \times 3.2 \times 30 $$

$$ \text{Area} = \frac{1}{2} \times 96 $$

$$ \text{Area} = 48 \, \text{m}^2 $$

Therefore, the area of the vertical cross-section of the pool is 48 m², which corresponds to Option 1.

Now, let's explain why the other options are incorrect:

- **Option 2 (72 m²):** This option is incorrect because it overestimates the area. The calculation using the trapezoidal formula clearly shows that the area is 48 m², not 72 m².

- **Option 3 (156 m²):** This option is incorrect as it significantly overestimates the area. The correct calculation yields 48 m², which is much less than 156 m².

- **Option 4 (192 m²):** This option is incorrect because it grossly overestimates the area. The correct area, as calculated, is 48 m², which is far less than 192 m².

In conclusion, the correct area of the vertical cross-section of the pool is 48 m², making Option 1 the correct choice.