Geometry

Question Analysis

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

 

Key Concept Explanation

The formula for the area of 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 central - angle measure to the full  of a circle, which determines the proportion of the sector's area to the area of the entire circle ().

 

Step - by - Step Solution

1. Calculate the radius: Since the diameter  meters, the radius  meters.

2. Substitute the values into the sector - area formula . We know  and . So the equation becomes .

3. Simplify the equation:

First, calculate

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