Circumference - Examples, Exercises and Solutions

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

Practice Circumference

Exercise #1

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Video Solution

Step-by-Step Solution

The formula for the circumference is equal to:

2πr 2\pi r

Answer

Exercise #2

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

888OOO What is its circumference?

Video Solution

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

Exercise #3

Look at the circle in the figure.

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

6

Video Solution

Step-by-Step Solution

Formula of the circumference:

P=2πr P=2\pi r

We replace the data in the formula:

P=2×6×π P=2\times6\times\pi

P=12π P=12\pi

Answer

12π 12\pi

Exercise #4

A circle has a circumference of 31.41.

What is its radius?

Video Solution

Step-by-Step Solution

To solve the exercise, first we must remember the circumference formula:

P=2πR P= 2\pi R

P is the circumference and Pi has a value of 3.14 (approximately).

We substitute in the known data:

31.41=23.141R 31.41=2\cdot3.141\cdot R

Keep in mind that the result can be easily simplified using Pi:

31.413.141=2R \frac{31.41}{3.141}=2R

10=2R 10=2R

Finally, we simplify by 2:

5=R 5=R

Answer

5

Exercise #5

A circle has a circumference of 50.25.

What is its radius?

Video Solution

Step-by-Step Solution

We use the formula:

P=2πr P=2\pi r

We replace the data in the formula:

50.25=3.14×2r 50.25=3.14\times2r

50.25=2×r×3.14 50.25=2\times r\times3.14

50.25=6.28r 50.25=6.28r

50.256.28=6.28r6.28 \frac{50.25}{6.28}=\frac{6.28r}{6.28}

r=8 r=8

Answer

8

Exercise #1

The circumference of a circle is 14.

How long is the circle's radius?

Video Solution

Step-by-Step Solution

We use in the formula:

P=2πr P=2\pi r

We replace the data in the formula:

14=2×π×r 14=2\times\pi\times r

We divide Pi by 2:

142π=2πr2π \frac{14}{2\pi}=\frac{2\pi r}{2\pi}

7π=r \frac{7}{\pi}=r

Answer

7π \frac{7}{\pi}

Exercise #2

Below is a circle bounded by a parallelogram:

36

All meeting points are tangential to the circle.
The circumference is 25.13.

What is the area of the parallelogram?

Video Solution

Step-by-Step Solution

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

AE=AF=3 AE=AF=3
BG=BF=6 BG=BF=6

And from here we can calculate:

AB=AF+FB=3+6=9 AB=AF+FB=3+6=9

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

Since the circumference is 25.13.

Circumference formula:2πR 2\pi R
We replace and solve:

2πR=25.13 2\pi R=25.13
πR=12.565 \pi R=12.565
R4 R\approx4

The height of the parallelogram is equal to two radii, that is, 8.

And from here you can calculate with a parallelogram area formula:

AlturaXLado AlturaXLado

9×872 9\times8\approx72

Answer

72 \approx72

Exercise #3

The following is a circle enclosed in a parallelogram:

36

All meeting points are tangent to the circle.
The circumference is 25.13.

What is the area of the zones marked in blue?

Video Solution

Step-by-Step Solution

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

AE=AF=3 AE=AF=3
BG=BF=6 BG=BF=6

From here we can calculate:

AB=AF+FB=3+6=9 AB=AF+FB=3+6=9

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

It is known that the circumference of the circle is 25.13.

Formula of the circumference:2πR 2\pi R
We replace and solve:

2πR=25.13 2\pi R=25.13
πR=12.565 \pi R=12.565
R4 R\approx4

The height of the parallelogram is equal to two radii, that is, 8.

And from here it is possible to calculate the area of the parallelogram:

Lado x Altura \text{Lado }x\text{ Altura} 9×872 9\times8\approx72

Now, we calculate the area of the circle according to the formula:πR2 \pi R^2

π42=50.26 \pi4^2=50.26

Now, subtract the area of the circle from the surface of the trapezoid to get the answer:

7256.2421.73 72-56.24\approx21.73

Answer

21.73 \approx21.73

Exercise #4

Given the circle whose radius has a length of 9 cm

999

What is its perimeter?

Video Solution

Answer

56.55

Exercise #5

A circle has a diameter of 12.

121212

What is its perimeter?

Video Solution

Answer

12π

Exercise #1

A circle has a radius of 3 cm.

What is its perimeter?

333

Video Solution

Answer

6π 6\pi cm

Exercise #2

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

Video Solution

Answer

8π 8\pi cm

Exercise #3

O is the center of the circle.

AB = 15

Is it possible to work out its circumference?

OOOBBBAAA15

Video Solution

Answer

Yes, 15π 15\pi cm

Exercise #4

Look at the circle in the figure.

Is it possible to calculate its circumference?

222

Video Solution

Answer

It is not possible to calculate.

Exercise #5

Look at the circle in the figure.

Given that its radius is equal to 3, what is its circumference?

3

Video Solution

Answer

6π 6\pi

Topics learned in later sections

  1. Circle
  2. Diameter
  3. The Center of a Circle
  4. Radius
  5. How is the radius calculated using its circumference?
  6. Perimeter
  7. Area
  8. Area of a circle