Geometry

Question Analysis

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

 

Key Concept Explanation

The formula for the area of a sector of a circle with central angle  (in radians) is , where  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, with the proportion determined by the central angle relative 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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