Geometry

Question Analysis

The main focus is applying the formula for the area of a ring. Given the outer radius of the frame and the inner radius of the painting, we need to calculate the difference between the areas of the outer and inner circles to find the area of the frame.

Key Concept Explanation

The area of a circle is given by , where  is the radius. For a ring (annulus), the area , with  being the outer radius and  being the inner radius. This formula subtracts the area of the inner circle from the area of the outer circle.

Step - by - Step Solution

1. Identify the outer and inner radii:

The outer radius  inches (radius of the frame).

The inner radius  inches (radius of the painting).

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

Substitute into .

Calculate  and .

Then

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