The volume of water measured on a rectangular field 500 m `xx` 300 m is 3000 `m^(3)`. Find the depth (amount) of rain that has fallen.

Options

A. 2 cms
B. 3 cms
C. 4 cms
D. 3.5 cms

Answer

To find the depth of rain that has fallen on a rectangular field, we can use the formula for the volume of a cuboid. The steps to solve the problem are as follows:

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangular field:**
- Length (L) = 500 m
- Breadth (B) = 300 m

2. **Given the volume of water collected:**
- Volume (V) = 3000 m³

3. **Use the formula for the volume of a cuboid:**
\[ V = L \times B \times H \]
Where H is the height (or depth of rain in this case).

4. **Substitute the known values into the formula:**
\[ 3000 = 500 \times 300 \times H \]

5. **Calculate the area of the base (Length × Breadth):**
\[ 500 \times 300 = 150000 \, m^2 \]

6. **Now, substitute this value back into the equation:**
\[ 3000 = 150000 \times H \]

7. **Solve for H (depth of rain):**
\[ H = \frac{3000}{150000} \]
\[ H = 0.02 \, m \]

8. **Convert the depth from meters to centimeters:**
\[ H = 0.02 \times 100 = 2 \, cm \]

### Final Answer:
The depth of rain that has fallen is **2 cm**.