# Radius

Understanding the radius is one of the most important elements of the geometry of the circle. The radius is a line segment with one endpoint at the center of the circle or sphere and the other at its boundary. The word may also refer to the length of such a line segment. Here is an example:

As you've previously learned, circles are defined as the set of all points in a plane at a given distance from the center. This means that all of the radii (the accepted plural form of radius) of a particular circle are the same length. Every circle has an infinite number of radii, and they can be named if specific points in the circle are labeled. Consider the following diagram:

In this example, PC, PB, and PA are all radii because they connect the origin point to a point on the outer boundary. Always put the origin point first when naming radii in this manner!

## Calculating the radius

The diameter is also closely related to the radius in that the diameter is a line segment containing the center and both endpoints. If you know the diameter, the radius is simply half of that value. Likewise, you can calculate the diameter of any circle by doubling its radius.

## Importance of radius

Again, you can also use the radius to find the diameter of a circle. Put simply, if you have the area, circumference, diameter, or radius of a circle, you can calculate all four values with a few formulas and a little bit of math.

## Radius practice questions

a. If a circle's diameter is expressed as 40 units, what is its radius?

b. If a circle's radius is expressed as 100 units, what is its diameter?

c. What is the radius of a circle with a circumference of 15 inches?

d. If AC and AB are both radii on the same circle and AB measures seven inches, what is the length of AC?

e. What is the area of a circle with a radius of 4 cm?

f. What is the circumference of a circle with a radius of 9 cm using 3.14 as the value of π?

g. What is the radius of a circle with an area of 379.94
cm^{2}?

## Topics related to the Radius

Perpendicular Transversal Theorem

## Flashcards covering the Radius

Common Core: High School - Geometry Flashcards

## Practice tests covering the Radius

Common Core: High School - Geometry Diagnostic Tests

Intermediate Geometry Diagnostic Tests

## Get help with concepts like radius today

The radius is a foundational concept in geometry and students who struggle with it are likely to feel overwhelmed by subsequent coursework as well. If the student in your life is falling behind their peers or you simply wish to equip them with an extra academic edge, contact the Educational Directors at Varsity Tutors right now to learn more about how 1-on-1 tutoring is one of the best ways for students of all ages and ability levels deepen their understanding of radii and related geometry concepts.

- Certified Ethical Hacker Test Prep
- Sociology Tutors
- Italian Tutors
- Film Studies Tutors
- GRE Test Prep
- Utah Bar Exam Test Prep
- Actuarial Exam P Test Prep
- CLEP Precalculus Test Prep
- Jewish Studies Tutors
- Series 99 Courses & Classes
- TEAS Tutors
- Exam IFM - Investment and Financial Markets Test Prep
- Six Sigma Training
- Digital Media Tutors
- SAT Subject Test in United States History Test Prep
- CISM - Certified Information Security Manager Training
- Mineralogy Tutors
- NASM - National Academy of Sports Medicine Courses & Classes
- CCNA Routing and Switching - Cisco Certified Network Associate-Routing and Switching Courses & Classes
- Wyoming Bar Exam Test Prep