Answer :
Final answer:
To find the circumference of the circle, you need to know the radius. You can find the radius using the formula for the area of a sector. Once you have the radius, you can use the formula for the circumference of a circle.
Explanation:
To find the circumference of the circle, we need to know the radius, not the area of a sector. However, we can use the given information to find the radius. The formula for the area of a sector is A = (θ/360) * π * r², where θ is the angle in degrees and r is the radius. We are given that the area of the sector is 25π square feet and the angle is 60 degrees. Plugging in these values, we get 25π = (60/360) * π * r². By simplifying the equation, we find that r² = 150/π. Taking the square root of both sides, we get r ≈ √(150/π) ≈ 6.178 feet.
Now that we have the radius, we can find the circumference of the circle using the formula C = 2πr. Plugging in the value of r, we get C = 2 * 3.14159 * 6.178 ≈ 38.779 feet. Therefore, the circumference of the circle is approximately 38.779 feet.
