CONCEPT PREVIEW Find the radius of each circle.

Verified step by step guidance

1. Step 1: Identify the given information about the circle, such as the diameter, circumference, or area.
2. Step 2: Recall the formulas related to the circle's radius: \( r = \frac{d}{2} \) for diameter \( d \), \( r = \frac{C}{2\pi} \) for circumference \( C \), and \( r = \sqrt{\frac{A}{\pi}} \) for area \( A \).
3. Step 3: Choose the appropriate formula based on the given information.
4. Step 4: Substitute the given values into the chosen formula.
5. Step 5: Solve the equation to find the radius of the circle.

Key Concepts

Circle Definition

A circle is a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is known as the radius. Understanding this definition is crucial for solving problems related to circles, including finding the radius when given other parameters.

Radius and Diameter Relationship

The radius of a circle is half the length of the diameter, which is the distance across the circle through its center. This relationship can be expressed mathematically as diameter = 2 × radius. Knowing this relationship allows for easy conversion between the two measurements when solving for the radius.

Circumference and Area Formulas

The circumference of a circle is the distance around it, calculated using the formula C = 2πr, where r is the radius. The area of a circle is given by A = πr². These formulas are essential for finding the radius when the circumference or area is provided, as they can be rearranged to solve for r.