Geometry

Question Analysis

The main focus is using the formula for the area of a sector when the area and radius are known, and then solving for the central angle in radians. We need to manipulate the sector - area formula to isolate the angle variable.

 

Key Concept Explanation

The area formula for a sector of a circle when the central angle  is in radians is , where  is the area of the sector,  is the radius of the circle, and  is the central angle in radians. This formula is based on the proportion of the sector's area to the area of the whole circle, with the proportion determined by the central angle relative to  (the full - circle angle in radians).

 

Step - by - Step Solution

1. Start with the sector - area formula .

2. We know that  and . Substitute these values into the formula: .

3. First, calculate

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