The amount of rice produced in a square field of side 50 m is 750 kg. The amount of rice produce in a similar square field of side 100 m will be

Options

A. 2000 kg
B. 3000 kg
C. 3500 kg
D. 1500 kg

Answer

To solve the problem of determining the amount of rice produced in a square field with a side of 100 m, given that a square field with a side of 50 m produces 750 kg of rice, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Area of the Fields:**
- The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
- For the first field with a side of 50 m:
\[ \text{Area}_{50} = 50^2 = 2500 \text{ m}^2 \]
- For the second field with a side of 100 m:
\[ \text{Area}_{100} = 100^2 = 10000 \text{ m}^2 \]

2. **Set Up a Ratio:**
- We know that the amount of rice produced is proportional to the area of the field. Thus, we can set up a ratio:
\[ \frac{\text{Amount of rice produced in 50 m field}}{\text{Area of 50 m field}} = \frac{\text{Amount of rice produced in 100 m field}}{\text{Area of 100 m field}} \]
- Let \( x \) be the amount of rice produced in the 100 m field. Then we have:
\[ \frac{750 \text{ kg}}{2500 \text{ m}^2} = \frac{x \text{ kg}}{10000 \text{ m}^2} \]

3. **Cross Multiply to Solve for \( x \):**
- Cross multiplying gives us:
\[ 750 \times 10000 = 2500 \times x \]
- This simplifies to:
\[ 7500000 = 2500x \]

4. **Solve for \( x \):**
- Divide both sides by 2500:
\[ x = \frac{7500000}{2500} \]
- Simplifying this gives:
\[ x = 3000 \text{ kg} \]

5. **Final Answer:**
- Therefore, the amount of rice produced in a similar square field of side 100 m is:
\[ \boxed{3000 \text{ kg}} \]