Geometry

Question Analysis

The main focus is using the formula for the area of a circle and fraction multiplication to find the area of the part of the circular mirror covered by the frame. Given the diameter of the mirror, we first find the radius, then calculate the total area of the mirror, and finally determine the area covered by the frame by multiplying the total area by the fraction representing the frame's portion.

Key Concept Explanation

The area of a circle is calculated by the formula , where is the radius. To find the area of a specific fraction of the circle, we multiply the fraction by the total area of the circle. Here, the fraction of the mirror surface covered by the frame is , so the area covered by the frame .

Step - by - Step Solution

1. Calculate the radius of the circular mirror. Since the diameter inches, the radius inches.

2. Find the total area of the circular mirror using the formula

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