Geometry

Question Analysis

The main focus is using the formula for the area of a sector with a central angle in radians. Given the diameter of the circle, we first find the radius, then use the sector - area formula with the known area to solve for the central angle in radians.

 

Key Concept Explanation

The formula for the area of a sector of a circle when the central angle  is in radians is , where  is the area of the sector,  is the radius, and  is the central angle. 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. Calculate the radius: Since the diameter  meters, the radius  meters.

2. Start with the sector - area formula .

3. Substitute  and  into the formula: .

4. Simplify

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