Circumference: Applying the formula

Increasing a specific element by addition of.....or multiplication by.......Using Pythagoras' theoremVerifying whether or not the formula is applicableSubtraction or addition to a larger shapeA shape consisting of several shapes (requiring the same formula)Using variablesCalculating parts of the circleIdentifying and defining elementsUsing additional geometric shapesWorded problemsIdentify the greater valueFinding Area based off Perimeter and Vice VersaCalculate The Missing Side based on the formula
Question 1

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

888OOO What is its circumference?

Question 2

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Question 3

Look at the circle in the figure.

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

6

Question 4

Look at the circle in the figure.

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

What is its perimeter?

Question 5

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: Applying the formula

Exercise #1

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 #2

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

8π

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 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

Exercise #4

Look at the circle in the figure.

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

What is its perimeter?

Video Solution

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

Exercise #5

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

Video Solution

Step-by-Step Solution

To solve this problem, we'll go through the following steps:

  • Calculate the circumference of the circular park.
  • Determine the total distance Ivan runs.
  • Find Ivan's average speed.

Step 1: Calculate the circumference of the circular park.
The formula for the circumference of a circle is C=2πr C = 2\pi r , where r r is the radius.
Given r=300 r = 300 meters, C=2π×300=600π C = 2\pi \times 300 = 600\pi meters.

Step 2: Determine the total distance Ivan runs.
Ivan completes 5 laps, so the total distance D D is given by:
D=5×600π=3000π D = 5 \times 600\pi = 3000\pi meters.

Step 3: Find Ivan's average speed.
The formula for average speed is v=total distancetotal time v = \frac{\text{total distance}}{\text{total time}} .
Total time = 35 minutes.
Average speed v=3000π35≈269.14 v = \frac{3000\pi}{35} \approx 269.14 meters per minute.

Therefore, Ivan's average speed is 269.14 269.14 meters per minute.

Answer

269.14 meter per minute

Question 1

\( r=11 \)

Calculate the circumference.

111111

Question 2

\( r=7 \)

Calculate the circumference.

777

Question 3

\( r=2 \)

Calculate the circumference.

222

Question 4

\( r=6 \)

Calculate the circumference.

666

Question 5

A circle has a radius of 3 cm.

What is its perimeter?

333

Exercise #6

r=11 r=11

Calculate the circumference.

111111

Video Solution

Answer

69.115

Exercise #7

r=7 r=7

Calculate the circumference.

777

Video Solution

Answer

43.982

Exercise #8

r=2 r=2

Calculate the circumference.

222

Video Solution

Answer

12.56

Exercise #9

r=6 r=6

Calculate the circumference.

666

Video Solution

Answer

37.699

Exercise #10

A circle has a radius of 3 cm.

What is its perimeter?

333

Video Solution

Answer

6π 6\pi cm

Question 1

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

Question 2

Given the circle whose radius has a length of 9 cm

999

What is its perimeter?

Question 3

A circle has a diameter of 12.

121212

What is its perimeter?

Question 4

Look at the circle in the figure.

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

3

Question 5

Look at the circle in the figure below.555

The radius of the circle equals 5.

What is its perimeter?

Exercise #11

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

Video Solution

Answer

8π 8\pi cm

Exercise #12

Given the circle whose radius has a length of 9 cm

999

What is its perimeter?

Video Solution

Answer

56.55

Exercise #13

A circle has a diameter of 12.

121212

What is its perimeter?

Video Solution

Answer

12π

Exercise #14

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

Exercise #15

Look at the circle in the figure below.555

The radius of the circle equals 5.

What is its perimeter?

Video Solution

Answer

10π 10\pi

Question 1

Look at the circle in the figure below.

The radius of the circle equals 7.

What is its perimeter?

777

Question 2

Look at the circle in the figure below.

The radius of the circle is equal to 8.

What is its perimeter?

888

Question 3

Look at the circle in the figure below.

The diameter of the circle is 4.

What is its perimeter?

444

Question 4

Look at the circle in the figure.

If its diameter is 5, then what is its circumference?

5

Question 5

Look at the circle in the figure.

The diameter of the circle is 10.

What is its perimeter?

101010

Exercise #16

Look at the circle in the figure below.

The radius of the circle equals 7.

What is its perimeter?

777

Video Solution

Answer

14π 14\pi

Exercise #17

Look at the circle in the figure below.

The radius of the circle is equal to 8.

What is its perimeter?

888

Video Solution

Answer

16π 16\pi

Exercise #18

Look at the circle in the figure below.

The diameter of the circle is 4.

What is its perimeter?

444

Video Solution

Answer

4π 4\pi

Exercise #19

Look at the circle in the figure.

If its diameter is 5, then what is its circumference?

5

Video Solution

Answer

5π 5\pi

Exercise #20

Look at the circle in the figure.

The diameter of the circle is 10.

What is its perimeter?

101010

Video Solution

Answer

10π 10\pi