Answer :
To find the area of the ring-shaped path around the flower garden, we can use the formula for the area of a ring or annulus, which is the difference between the areas of two concentric circles.
Let's denote:
- \( r_1 \) as the radius of the outer circle (outer edge of the path).
- \( r_2 \) as the radius of the inner circle (inner edge of the path).
- \( w \) as the width of the path.
Given:
- Radius of the garden, \( r_1 = 20 \) yd.
- Width of the path, \( w = 5 \) yd.
The radius of the inner circle, \( r_2 \), is the radius of the garden minus the width of the path:
\[ r_2 = r_1 - w = 20 \, \text{yd} - 5 \, \text{yd} = 15 \, \text{yd} \]
Now, we can calculate the areas of the outer and inner circles using the formula \( A = \pi r^2 \):
- Area of the outer circle:
\[ A_1 = \pi r_1^2 = \pi (20 \, \text{yd})^2 \]
- Area of the inner circle:
\[ A_2 = \pi r_2^2 = \pi (15 \, \text{yd})^2 \]
The area of the ring-shaped path is the difference between the areas of the outer and inner circles:
\[ \text{Area of path} = A_1 - A_2 \]
Let's calculate the values and find the area of the path.
