Geometry

Question Analysis

The main focus is applying the formula for the area of a ring. We need to determine the outer and inner radii of the ring - shaped walkway. The inner radius is the radius of the swimming pool, and the outer radius is the radius of the pool plus the width of the walkway. Then, we calculate the difference between the areas of the outer and inner circles.

Key Concept Explanation

The area of a circle is , where  is the radius. For a ring (annulus), the area , with  as the outer radius and  as the inner radius. The formula works by subtracting the area of the inner circle from the area of the outer circle.

Step - by - Step Solution

1. Identify the inner and outer radii:

The inner radius  (radius of the pool) is 15 meters.

The outer radius  meters.

2. Apply the formula for the area of the ring:

Substitute into .

Calculate  and