Geometry

Question Analysis

The main focus is using the formula for the area of a sector when the central angle is given in radians. We need to substitute the radius and the central - angle values into the appropriate formula to find the area of the sector.

 

Key Concept Explanation

The area formula for a sector of a circle when the central angle  is in radians is , where  is the radius of the circle. This formula is derived from the relationship between the sector's area, the circle's area, and the proportion of the central angle to  (the full - circle angle in radians).

 

Step - by - Step Solution

1. Identify the values: The radius  and the central angle .

2. Substitute into the formula .

First, calculate .

Then,

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