Calculating Rain Volume

The question asks for the total volume of rain in cubic meters over a one-hectare field, given the depth of rain is 10 cm. To find the volume, we need to multiply the area of the field by the depth of the rain. We must ensure all measurements are in compatible units, specifically meters, to get the final volume in cubic meters.

Unit Conversions

The given area is 1 hectare. We need to convert hectares to square meters.

• 1 hectare is equal to 10,000 square meters ($1 \text{ hectare} = 10,000 \text{ m}^2$).

The given depth of rain is 10 cm. We need to convert centimeters to meters.

• 1 meter is equal to 100 centimeters ($1 \text{ m} = 100 \text{ cm}$).
• Therefore, 1 centimeter is equal to 0.01 meters ($1 \text{ cm} = 0.01 \text{ m}$).

So, the depth of rain in meters is:

$\text{Depth} = 10 \text{ cm} \times 0.01 \frac{\text{m}}{\text{cm}} = 0.1 \text{ m}$

Volume Calculation

Now we can calculate the total volume of rain using the formula for the volume of a rectangular prism (although the field isn't necessarily a perfect rectangle, the principle of area × height applies):

$\text{Volume} = \text{Area} \times \text{Depth}$

Using the converted values:

$\text{Volume} = 10,000 \text{ m}^2 \times 0.1 \text{ m}$

$\text{Volume} = 1000 \text{ m}^3$

The total volume of rain over the one-hectare field is 1000 cubic meters.