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Radius

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Radius

Study Guide

Key Definition

The radius is a line segment from the center of a circle to its boundary, denoted by $r$.

Important Notes

The radius is half of the diameter: $r = \frac{d}{2}$
All radii of a circle are equal in length
The formula for the radius given circumference is $r = \frac{C}{2\pi}$
The formula for the radius given area is $r = \sqrt{\frac{A}{\pi}}$
The radius is a fundamental element of circle geometry
Named radii are denoted by the center point first, e.g., $\overline{CP}$

Mathematical Notation

$\pi$ represents pi, approximately 3.14

$\frac{a}{b}$ represents a fraction

$\sqrt{x}$ represents the square root

Remember to use proper notation when solving problems

Why It Works

The radius helps in understanding the properties of circles, and $r = \frac{C}{2\pi}$ connects circumference and radius.

Remember

The radius is a key measurement for calculating the area and circumference of circles.

Quick Reference

Radius Formula:$r = \frac{C}{2\pi}$

Understanding Radius

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The radius is half the diameter: $r = \frac{d}{2}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the radius of a circle with a diameter of $10$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A giant pizza with a circumference of $31.4$ inches has been ordered. What is the radius?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given a circle with circumference $50$, find the radius.

Challenge Quiz

Single Choice Quiz

Advanced

If the area of a circle is $64\pi$, what is the radius?

Recap

Watch & Learn

Review key concepts and takeaways