Which figure shows the radius of a circle?

Parts of a Circle Practice Problems: Radius, Diameter & Area

Master circle geometry with interactive practice problems on radius, diameter, circumference, and area calculations. Step-by-step solutions included.

📚What You'll Practice and Master

Calculate radius from given diameter measurements using the relationship r = d/2
Find circumference using the formula C = 2πr with various radius values
Determine circle area using A = πr² formula with step-by-step solutions
Solve for radius when given circumference or area measurements
Compare perimeters of circles and squares to understand relative sizes
Work with fractional and decimal radius measurements in real problems

Understanding Radius

Complete explanation with examples

The radius is one of the many elements that exist in a circle. The radius is a segment that connects the center of the circle with any point located on the circle itself. Each circle has an infinite number of radii and their length is exactly the same, that is, they are identical.

The radius is used to calculate the diameter and perimeter of the circle, it is also used to obtain the area of the circle.

Below are several examples of different circumferences.

The colored parts are, in fact, some radii painted on each circumference:

The colored parts are, in fact, some painted radii on the circumference:

Radius

Detailed explanation

Practice Radius

Test your knowledge with 11 quizzes

True or false:

The radius of a circle is the chord.

Examples with solutions for Radius

Step-by-step solutions included

Exercise #1

There are only 4 radii in a circle.

Step-by-Step Solution

A radius is a straight line that connects the center of the circle with a point on the circle itself.

Therefore, the answer is incorrect, as there are infinite radii.

Answer:

False

Exercise #2

If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.

Step-by-Step Solution

To determine if the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is true, we need to use the relationship between the radius and diameter of a circle.

The diameter $d$ of a circle is calculated using the formula:

$d = 2r$

where $r$ is the radius. In this problem, the radius $r$ is given as 5 cm.

Using the formula, the diameter is:

$d = 2 \times 5 \, \text{cm} = 10 \, \text{cm}$

This matches exactly the length of the diameter given in the problem.

Therefore, the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is True.

Answer:

True

Exercise #3

The number Pi $(\pi)$ represents the relationship between which parts of the circle?

Step-by-Step Solution

To solve this problem, we will clarify the relationship between the constant $\pi$ and parts of a circle.

The number $\pi$ is a constant that relates the circumference of a circle (the perimeter) to its diameter. The formula for the circumference $C$ of a circle is given by:

C = \pi \times d

where $C$ is the circumference, and $d$ is the diameter of the circle. This equation shows that $\pi$ is the ratio of the circumference of a circle to its diameter, which remains constant for all circles.

Therefore, $\pi$ indeed represents the relationship between the circle’s perimeter and its diameter.

Thus, the correct answer is: Perimeter and diameter

Answer:

Perimeter and diameter

Exercise #4

M is the center of the circle.

Perhaps $AB=CD$

Step-by-Step Solution

CD is a diameter, since it passes through the center of the circle, meaning it is the longest segment in the circle.

AB does not pass through the center of the circle and is not a diameter, therefore it is necessarily shorter.

Therefore:

$AB\ne CD$

Answer:

Video Solution

Exercise #5

Which diagram shows a circle with a point marked in the circle and not on the circle?

Step-by-Step Solution

The interpretation of "in a circle" is inside the circle.

In diagrams (a) and (d) the point is on the circle, while in diagram (c) the point is outside of the circle.

Answer:

Frequently Asked Questions

Everything you need to know about Radius

What is the radius of a circle and how do I find it?

The radius is a line segment from the center of a circle to any point on the circle's edge. To find the radius: divide the diameter by 2, use r = C/(2π) if you know circumference, or use r = √(A/π) if you know the area.

How do you calculate the circumference of a circle using radius?

Use the formula C = 2πr where C is circumference, π ≈ 3.14, and r is the radius. For example, if radius = 5 cm, then C = 2 × 3.14 × 5 = 31.4 cm.

What's the difference between radius and diameter of a circle?

The radius goes from the center to the edge of the circle, while the diameter goes all the way across the circle through the center. The diameter is always exactly twice the length of the radius: d = 2r.

How do I find the area of a circle when I know the radius?

Use the formula A = πr² where A is area, π ≈ 3.14, and r is radius squared. Steps: 1) Square the radius value, 2) Multiply by π (3.14), 3) Include units² in your answer.

Can I find the radius if I only know the circle's area?

Yes! Use the formula r = √(A/π). Steps: 1) Divide the area by π (3.14), 2) Take the square root of that result. For example, if area = 64 cm², then r = √(64/3.14) = √20.38 ≈ 4.5 cm.

What are common mistakes when working with circle radius problems?

Common errors include: confusing radius with diameter, forgetting to square the radius in area formulas, using wrong units (cm vs cm²), and not using π correctly in calculations.

How do radius measurements work with fractions?

Fractional radii work the same way as whole numbers. If radius = 1/4, then circumference = 2π(1/4) = π/2. For area with fractional radius, square the fraction first: A = π(1/4)² = π/16.

Why do we use π in circle formulas and what value should I use?

π (pi) represents the ratio of any circle's circumference to its diameter, approximately 3.14159. For most problems, use π ≈ 3.14. Some answers are left in terms of π (like 6π cm) for exact values.

Continue Your Math Journey

Master Radius first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Circle Diameter Pi The Circumference of a Circle The Center of a Circle How is the radius calculated using its circumference?Perimeter Parts of a Circle Area Elements of the circumference Area of a circle

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Calculating the size Determine whether or not it is possible to draw Identifying and defining elements True / false Value of Pi