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 formula to find the area of the sector.

 

Key Concept Explanation

The area of a sector of a circle with central angle  (in degrees) is given by , where  is the radius of the circle. This formula is based on the proportion of the sector's central 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: .

3. First, calculate