Find the area of the shaded portion of the circle. The radius of the circle is 9 inches. (GRAPH

step 1 We need to find the area of the shaded portion of the circle. So the shaded portion of the circl

Find the area of the shaded portion of the circle. The...

Key Concepts

Sector of a Circle

A sector of a circle is a region bounded by two radii and the arc between them, resembling a 'slice' of the circle. When a specific angle is given or implied, the sector's area can be determined by taking the corresponding fraction of the full circle's area, usually using the formula (?/360°) × ?r² for degrees or (?/2?) × ?r² for radians.

Area of a Circle

The area of a circle quantifies the amount of space enclosed within its boundary. It is calculated using the formula A = ?r², where r is the radius. This formula is fundamental in problems where portions of a circle, such as sectors or segments, need to be analyzed or where area comparisons are involved.

Shaded Region in Circular Figures

In many geometry problems, the shaded region represents a specific part of the circle that needs to be isolated for calculation, such as a sector, segment, or a composite area formed by subtracting one shape from another. Identifying which part of the circle is shaded and how it is related to the full circle is crucial for applying the appropriate formula to compute its area.

Circle

A circle is a set of points in a plane that are equidistant from a central point. In problems involving circles, understanding the basic properties—such as radius, diameter, circumference, and area—is essential for calculating different portions of the circle or understanding its geometry.

Radius

The radius of a circle is the fixed distance between the center of the circle and any point on its boundary. It plays a vital role in many circle-related formulas, including the area of the circle (given by ? times the square of the radius) and the circumference (given by 2? times the radius).

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