Open Response The exact circumference of a circle is \( 34 \pi \) meters. What is the approximate area of the circle? Use 314 for \( \pi \). Round to the nearest hundredth if necessary.

To find the approximate area of the circle given its circumference, we can follow these steps: 1. **Extract known conditions:** - The circumference \( C \) of the circle is given as \( 34 \pi \) meters. - We will use \( \pi \approx 314 \). 2. **Use the formula for circumference:** The formula for the circumference of a circle is given by: \[ C = 2 \pi r \] where \( r \) is the radius of the circle. 3. **Solve for the radius \( r \):** We can rearrange the formula to solve for \( r \): \[ r = \frac{C}{2 \pi} \] Substituting the given circumference: \[ r = \frac{34 \pi}{2 \pi} = \frac{34}{2} = 17 \text{ meters} \] 4. **Calculate the area \( A \) of the circle:** The area of a circle is given by the formula: \[ A = \pi r^2 \] Substituting the radius we found: \[ A = \pi (17)^2 = \pi \cdot 289 \] 5. **Substituting \( \pi \) with 314:** \[ A \approx 314 \cdot 289 \] 6. **Perform the multiplication:** Now, we will calculate \( 314 \cdot 289 \): \[ A \approx 314 \cdot 289 \] Let's calculate this value. Calculate the value by following steps: - step0: Calculate: \(314\times 289\) - step1: Multiply the numbers: \(90746\) The approximate area of the circle is \( 90746 \) square meters. Since the problem does not require rounding to the nearest hundredth, the final answer is: **The approximate area of the circle is \( 90746 \) square meters.**