Geometry

Question Analysis

The main focus is applying the formula for the area of a sector when the central angle is given in degrees. We need to substitute the radius and the central - angle values into the appropriate formula to find the area of the sector.

 

Key Concept Explanation

The formula for the area of a sector of a circle when the central angle  is in degrees is , where  is the area of the sector,  is the central angle, and  is the radius of the circle. This formula is based on the proportion of the sector's angle to the full  of a circle, which determines the proportion of the sector's area to the area of the whole circle ().

 

Step - by - Step Solution

1. Identify the values: The radius  and the central angle .

2. Substitute into the formula .

First, calculate