What is a Radius?

In geometry, a radius is a straight line from the center of a circle to any point on the circle's circumference. It is a fundamental measurement in understanding the properties and characteristics of circles.

How to Find the Radius

There are a few different ways to find the radius of a circle:

1. Given the Diameter: If you are given the diameter of a circle, you can find the radius by dividing the diameter by 2. The formula is: radius = diameter / 2.
2. Given the Circumference: If you are given the circumference of a circle, you can find the radius using the formula: radius = circumference / (2 * π), where π (pi) is approximately 3.14159.
3. Given the Area: If you are given the area of a circle, you can find the radius using the formula: radius = √(area / π).

Properties of the Radius

Understanding the radius is essential for understanding the properties of circles. Some important properties of the radius include:

• The radius is always half the length of the diameter.
• All radii of a circle are congruent (have the same length).
• The radius is used to calculate the circumference, area, and other measurements of a circle.

Practice Questions

Now that you understand the concept of radius, here are some practice questions to test your knowledge:

1. Find the radius of a circle with a diameter of 10 units.
2. If the circumference of a circle is 31.4 units, what is the radius?
3. The area of a circle is 64π square units. What is the radius?

Answers

1. Given the diameter, the radius is: radius = 10 / 2 = 5 units.
2. Given the circumference, the radius is: radius = 31.4 / (2 * π) ≈ 5 units.
3. Given the area, the radius is: radius = √(64π / π) = 8 units.

Hope this study guide helps you understand the concept of radius in geometry!