Geometry

Question Analysis

The main focus is using the sector - area formula to find the central angle of the sector. Given the radius and the area of the sector, we need to rearrange the formula to solve for the unknown angle.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Start with the sector - area formula .

2. Substitute  and  into the formula: .

3. First, simplify