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

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

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:

Exercise #2

Which figure shows the radius of a circle?

Step-by-Step Solution

It is a straight line connecting the center of the circle to a point located on the circle itself.

Therefore, the diagram that fits the definition is c.

In diagram a, the line does not pass through the center, and in diagram b, it is a diameter.

Answer:

Exercise #3

All ____ about the circle located in the distance ____ from the ____ circle

Step-by-Step Solution

To solve this problem, we will consider the parts of a circle and how they interplay based on the description provided in the incomplete sentence:

Step 1: Recognize that the first blank needs a term that refers to the primary element defining a circle externally.
Step 2: The second blank needs a term associated with 'equal' as it describes distances from a specific location, hinting at a property of circles.
Step 3: The third blank likely wants us to relate this location to the circle itself, denoting the standard geometric reference point.

Now, let's fill in each blank systematically:

The first term 'Point' refers to all points lying on the perimeter of a circle. In the definition of a circle, each point on the circle’s circumference maintains an equal distance from its center.

The second term 'equal' pertains to how all these points are at an equal distance - which is the radius - from the center.

The third term 'center' specifies the reference point within the circle from which every point on the circle is equidistant.

Thus, the complete statement is: "All point about the circle located in the distance equal from the center circle."

The correct choice that completes the sentence is: Point, equal, center.

Answer:

Point, equal, center

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

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

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

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