Geometry

Question Analysis

The main focus is applying the formula for the area of a ring. Given the outer radius of the clock dial and the inner radius of the ring formed by the hour and minute markers, we need to calculate the difference between the areas of the outer and inner circles.

Key Concept Explanation

The area of a circle is calculated 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 clock dial).

The inner radius  inches (radius of the ring formed by the markers).

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

Substitute into .

Calculate  and .

Then

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