Circumference - Examples, Exercises and Solutions

Understanding Circumference

Complete explanation with examples

The circumference is actually the length of the circular line. It is calculated by multiplying the radius by 2, which has an approximate value of π. It can also be said that the circumference is equal to the the diameter of the circumference multiplied by π (since the diameter is actually twice the radius of the circumference). It is customary to identify the circumference (the perimeter) with the letter P.

The formula for calculating the circumference is:

P=2×π×R P=2\times\pi\times R

We will illustrate the concept with a simple example. Here is a circle, as shown in the drawing in front of you:

C - perimeter of the circumference

The radius of the circumference is 3 cm 3\text{ cm} .

You can calculate the circumference of the circle by placing the data:

P=2×R×π=2×3×3.14=18.84 P=2\times R\timesπ=2\times3\times3.14=18.84

That is, the circumference is 18.84 cm 18.84\text{ cm} .


Detailed explanation

Practice 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 Circumference

Step-by-step solutions included
Exercise #1

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 #2

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 #3

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 #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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