To fill a rectangular tank of area 700 m$^2$, 140m$^3$ of water is required. What will be the height of the water level in the tank?

Question

Accepted Answer

To determine the height of the water level in the tank, we need to use the formula for the volume of a rectangular prism (or tank), which is given by:

$$ \text{Volume} = \text{Area of the base} \times \text{Height} $$

In this problem, we are given:
- The area of the base of the tank = 700 m²
- The volume of water required to fill the tank = 140 m³

We need to find the height of the water level, which can be calculated by rearranging the formula:

$$ \text{Height} = \frac{\text{Volume}}{\text{Area of the base}} $$

Substituting the given values:

$$ \text{Height} = \frac{140 \, \text{m}^3}{700 \, \text{m}^2} $$

$$ \text{Height} = 0.2 \, \text{m} $$

Since the options are given in centimeters, we need to convert the height from meters to centimeters:

$$ 0.2 \, \text{m} = 20 \, \text{cm} $$

Therefore, the height of the water level in the tank is 20 cm, which corresponds to Option 2.

**Explanation for why each of the other options is incorrect:**

1. **Option 1 (10 cm):** This option suggests that the height of the water level is 10 cm. However, as calculated, the correct height is 20 cm. Therefore, 10 cm is too low and does not match the calculated height.

2. **Option 3 (30 cm):** This option suggests a height of 30 cm. Since the calculated height is 20 cm, 30 cm is too high and does not correspond to the given volume and area.

3. **Option 4 (40 cm):** This option suggests a height of 40 cm. Again, the calculated height is 20 cm, so 40 cm is significantly higher than the correct height and does not fit the given parameters.

In conclusion, the correct height of the water level in the tank is 20 cm, which is why Option 2 is the correct answer.