In Problems 79-86, A denotes the area of the sector of a...

In Problems $79-86,$ A denotes the area of the sector of a circle of radius r formed by the central angle $\theta .$ Find the missing quantity. Round answers to three decimal places.
$$\theta=\frac{1}{4} \text { radian, } \quad A=6 \text { square centimeters, } \quad r=?$$

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Key Concepts

Algebraic Manipulation in Geometric Formulas

This concept involves rearranging and solving equations that represent geometric relationships. In the context of the area of a circular sector, algebraic manipulation is used to isolate and solve for unknown quantities, such as the radius when the area and central angle are given.

Circular Sector

A circular sector is the portion of a circle enclosed by two radii and the connecting arc. It is a fundamental concept in geometry, often used to describe parts of a circle and to solve problems involving angles and lengths within circles.

Area of a Circular Sector

The area of a circular sector is determined by the formula A = ½ r²?, where r is the radius of the circle and ? is the central angle in radians. This formula is a key tool in relating the measure of an angle to a portion of the overall area of the circle.

Radian Measure

Radian measure is a standard way of measuring angles based on the radius of the circle. One radian is the angle created when the arc length from the center is equal to the radius. Using radians in formulas such as the area of a circular sector simplifies many trigonometric and geometric computations.

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