Questions: Jose is adding mulch to an existing round flower bed. The length of the rubber edging around the flower bed is 25.12 feet. What is the area that Jose needs to cover with mulch?

Solution Steps

To find the area that Jose needs to cover with mulch, we need to determine the radius of the flower bed first. The length of the rubber edging around the flower bed is the circumference of the circle. We can use the formula for the circumference of a circle, \( C = 2\pi r \), to find the radius \( r \). Once we have the radius, we can use the formula for the area of a circle, \( A = \pi r^2 \), to find the area.

1. Use the circumference formula \( C = 2\pi r \) to solve for the radius \( r \).
2. Use the radius to calculate the area using the formula \( A = \pi r^2 \).

Given the circumference \( C = 25.12 \) feet, we use the formula for the circumference of a circle: \[ C = 2\pi r \] Solving for \( r \): \[ r = \frac{C}{2\pi} = \frac{25.12}{2\pi} \approx 3.998 \text{ feet} \]

Using the radius \( r \approx 3.998 \) feet, we calculate the area \( A \) of the circle using the formula: \[ A = \pi r^2 \] Substituting the value of \( r \): \[ A = \pi (3.998)^2 \approx 50.21 \text{ square feet} \]

Final Answer