What length of rope is required, if 6 rounds of rope are needed to put around the fence of a circular track of radius 490 m.

Answer

To find the length of rope required to put around the fence of a circular track with a radius of 490 meters, and given that 6 rounds of rope are needed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the total length of rope required for 6 rounds around a circular track.

2. **Calculate the Circumference of the Circle**: The circumference (C) of a circle can be calculated using the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle. Given that the radius \( r = 490 \) meters, we can use \( \pi \approx \frac{22}{7} \) for our calculations.

3. **Substitute the Radius into the Formula**:
\[ C = 2 \times \frac{22}{7} \times 490 \]

4. **Simplify the Calculation**:
- First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
- Now, substitute this back into the circumference formula:
\[ C = \frac{44}{7} \times 490 \]

5. **Perform the Multiplication**:
- To simplify \( \frac{44}{7} \times 490 \), we can divide 490 by 7:
\[ 490 \div 7 = 70 \]
- Now multiply:
\[ C = 44 \times 70 = 3080 \text{ meters} \]

6. **Calculate the Total Length of Rope for 6 Rounds**:
- Since we need 6 rounds of rope, we multiply the circumference by 6:
\[ \text{Total Length} = 6 \times 3080 \]

7. **Perform the Final Multiplication**:
\[ \text{Total Length} = 18480 \text{ meters} \]

### Final Answer:
The total length of rope required is **18480 meters**.