Find the circumference of the circle if the area of the circle is \( 333.1 \mathrm{ft}^{2} \). Use 3.14 as the value of \( \pi \). Select one: a. 32.4 ft b. 64.7 ft c. 66 ft d. 71 ft

To find the circumference of the circle, we first need to determine its radius from the area formula. The area \( A \) of a circle is given by: \[ A = \pi r^2 \] Given that the area is \( 333.1 \, \text{ft}^2 \) and using \( \pi \approx 3.14 \): \[ 333.1 = 3.14 r^2 \] Now, divide both sides by \( 3.14 \): \[ r^2 = \frac{333.1}{3.14} \approx 106.1 \] Next, we take the square root to find the radius: \[ r \approx \sqrt{106.1} \approx 10.3 \, \text{ft} \] Now we can find the circumference \( C \), which is given by: \[ C = 2\pi r \] Substituting the values we have: \[ C \approx 2 \times 3.14 \times 10.3 \approx 64.7 \, \text{ft} \] Thus, the correct answer is **b. 64.7 ft**. For a bit more context, the relationship between the area and circumference highlights the elegance of circles in geometry—where one property leads you seamlessly to another! And remember, using approximations like \( \pi \approx 3.14 \) can be useful for quick calculations, but it might lead to slight variations in more precise applications.