How is the radius calculated using its circumference? - Examples, Exercises and Solutions

Understanding How is the radius calculated using its circumference?

Complete explanation with examples

Some of you may know the radius as a "dial". Either way, the meaning is identical with the same characteristics. So, what is the radius? It is a specific segment that connects the center of a circle with a particular point on the circumference .

How is the radius calculated using its perimeter?

The formula for calculating the perimeter or circumference of a circle is: P=2πR P=2πR

Where P= P = is the perimeter of the circle, R= R = is the radius of the circle, and π= π = is a number approximately equal to 3.14 3.14 .

Given: A circle with a circumference of 18.84 18.84 . The radius of the circle needs to be calculated.

We will place the known data into the formula: 18.84=2πR 18.84=2πR

The perimeter can be translated in terms of π π , that is: 18.84:3.14=6 18.84:3.14=6

Then we obtain: 6π=2πR 6π=2πR

Reduce the value of π π and get 6=2R 6=2R . Continue with a division by 2 2 to isolate the value of R R .

That is: R=62 R=\frac{6}{2} and, therefore, the result obtained is that the radius of the circle =3 =3 .

1 - How to calculate the radius using its perimeter

Detailed explanation

Practice How is the radius calculated using its circumference?

Test your knowledge with 30 quizzes

Ivan does laps around a circular park which has a radius of 300 meters.

He completes 5 full circuits in 35 minutes.

What was Ivan's average speed?

300300300

Examples with solutions for How is the radius calculated using its circumference?

Step-by-step solutions included
Exercise #1

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Step-by-Step Solution

The formula for the circumference is equal to:

2πr 2\pi r

Answer:

Video Solution
Exercise #2

O is the center of the circle in the figure below.

888OOO What is its circumference?

Step-by-Step Solution

We use the formula:P=2πr P=2\pi r

We replace the data in the formula:P=2×8π P=2\times8\pi

P=16π P=16\pi

Answer:

16π 16\pi cm

Video Solution
Exercise #3

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

6

Step-by-Step Solution

Formula of the circumference:

P=2πr P=2\pi r

We insert the given data into the formula:

P=2×6×π P=2\times6\times\pi

P=12π P=12\pi

Answer:

12π 12\pi

Video Solution
Exercise #4

Look at the circle in the figure.

The radius of the circle is 23 \frac{2}{3} .

What is its perimeter?

Step-by-Step Solution

The radius is a straight line that extends from the center of the circle to its outer edge.

The radius is essential for calculating the circumference of the circle, which can be found using the following formula:

If we substitute in the radius we have, the formula will be:

2*π*2/3

To solve this, first we'll rearrange the formula like so:

π*2*2/3 =

We'll then multiply the fraction by the whole number:

π*(2*2)/3 =

π*4/3 =

4/3π

Answer:

43π \frac{4}{3}\pi

Video Solution
Exercise #5

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

Step-by-Step Solution

To calculate, we will use the formula:

P2r=π \frac{P}{2r}=\pi

Pi is the ratio between the circumference of the circle and the diameter of the circle.

The diameter is equal to 2 radii.

Let's substitute the given data into the formula:

84=π \frac{8}{4}=\pi

2π 2\ne\pi

Therefore, this situation is not possible.

Answer:

Impossible

Video Solution

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