Circumference Length Exercises

Many problems involving circularly shaped things or objects boil down to calculating the circumference length.

The length C of a circle can be calculated by the following formula:

$\dpi{120} \mathrm{C = 2\cdot \pi \cdot r}$

Where r is the measure of the radius of the circumference.

To learn more about this topic, check out a list of circumference length exercises, all resolved and with feedback.

Index

List of exercises on circumference length
Resolution of question 1
Resolution of question 2
Resolution of question 3
Resolution of question 4
Resolution of question 5
Resolution of question 6

List of exercises on circumference length

Question 1. You want to sew a decorative ribbon around the lid of a round pot. If the diameter of the lid measures 12 cm, what is the minimum length of the tape to go all the way around the lid?

Question 2. The outline of a circular piece is 190 cm long. What is the diameter of this part?

Question 3. The wheel of a bus is 90 cm in radius. How far will the bus have traveled when the wheel makes 120 turns?

Question 4. What is the area of a circle whose circumference is 40 meters long?

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Question 5. A circle is 18 cm² in area. What is your perimeter?

Question 6. The surface of a table is formed by a square with a side equal to 2 m and two semicircles, one on each side, as shown in the figure.

circumference length - perimeter - exercise

Calculate the perimeter and surface area of the table.

Resolution of question 1

The measure of the pot's contour corresponds to the length of a circumference with a diameter equal to 12 cm.

To calculate the length, we need the radius.

The radius of a circle is equal to half the diameter measurement, so the radius is equal to 6 cm.

Replacing r by 6 and $\dpi{120} \pi$ by 3.14, in the formula for the circumference length, we have to:

$\dpi{120} \mathrm{C = 2\cdot 3.14 \cdot 12}$

$\dpi{120} \Rightarrow \mathrm{C = 75.36}$

As the radius measurement is in centimeters, the length result will also be in centimeters.

Therefore, the tape must be at least 75.36 centimeters long to go all the way around the lid of the pot.

Resolution of question 2

Knowing the measure of the length of a circle, we can determine the radius value.

See that replacing C by 190 and $\dpi{120} \pi$ by 3.14 in the formula, we have to:

$\dpi{120} \mathrm{190 = 2\cdot 3.14 \cdot r}$

$\dpi{120} \Rightarrow \mathrm{190 = 6.28\cdot r}$

$\dpi{120} \Rightarrow \mathrm{r = 30.24}$

With the radius measurement, we can determine the diameter.

$\dpi{120} \mathrm{D = 2\cdot r}$

$\dpi{120} \Rightarrow \mathrm{D = 2\cdot 30.24}$

$\dpi{120} \Rightarrow \mathrm{D = 60.48}$

As the length measurement was given in centimeters, then the calculated radius and diameter are also in centimeters.

Thus, the diameter of the piece measures 60.48 cm.

Resolution of question 3

On each turn the wheel makes, the distance traveled is equal to the length of the wheel's contour.

So what we have to do is calculate that length and then multiply that value by 120, which is the total number of turns.

Replacing r by 90 and $\dpi{120} \pi$ by 3.14 in the length formula, we get:

$\dpi{120} \mathrm{C = 2\cdot 3.14 \cdot 90}$

$\dpi{120} \Rightarrow \mathrm{C = 565.2}$

So, the length of the wheel contour is equal to 565.2 cm.

Let's multiply by 120 to get the distance covered:

565,2 × 120 = 67824

Until now, we used measurements in centimeters, so the result is also in centimeters.

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To indicate the distance traveled by the bus, let's do the transformation to meters:

67824: 100 = 678,24

Therefore, the distance covered by the bus was 678.24 meters.

Resolution of question 4

THE circle area depends on the radius measurement.

To find out the radius measure, let's use the circumference length information:

$\dpi{120} \mathrm{40 = 2\cdot 3.14 \cdot r}$

$\dpi{120} \Rightarrow \mathrm{40 = 6.28 \cdot r}$

$\dpi{120} \Rightarrow \mathrm{r = 6.37}$

Now we can calculate the area of the circle:

$\dpi{120} \mathrm{A = \pi\cdot r^2}$

$\dpi{120} \Rightarrow \mathrm{A =3.14\cdot (6.37)^2}$

$\dpi{120} \Rightarrow \mathrm{A =127.4}$

The measurements used were in meters, so the area will be in meters squared. Therefore, the area of the circle is equal to 127.4 m².

Resolution of question 5

The perimeter of a circle corresponds to the measure of its outline, which is the length of the circumference.

The length of the circle depends on the radius value. To determine this value, let's use the circle area information:

$\dpi{120} \mathrm{A = \pi\cdot r^2}$

$\dpi{120} \Rightarrow \mathrm{18 =3.14\cdot r^2}$

$\dpi{120} \Rightarrow \mathrm{r^2 = \frac{18}{3.14}}$

$\dpi{120} \Rightarrow \mathrm{r^2 = 5.7325}$

$\dpi{120} \Rightarrow \mathrm{r = 2.393}$

Now that we know the radius measurement, we can calculate the length of the circle:

$\dpi{120} \mathrm{C = 2\cdot 3.14 \cdot 2.393}$

$\dpi{120} \Rightarrow \mathrm{C = 15.01}$

Therefore, the length of the circumference (circle perimeter) is equal to 15.01 cm.

Resolution of question 6

The perimeter corresponds to the measure of the outline of the figure. So, just calculate the perimeter of the circle and add it with both sides of the square.

Perimeter of the circle:

The circle has a diameter equal to 2 (it is the side of the square), so the radius is equal to 1.

By the formula for the length of the circle, we have to:

$\dpi{120} \mathrm{C = 2\cdot 3.14 \cdot 1}$

$\dpi{120} \mathrm{C = 6.28}$

Which means the circle is 6.28 meters in perimeter.

Perimeter of table surface:

P = 6.28 + 2 + 2

P = 10.28

Therefore, the perimeter of the surface of the table measures 10.28 meters.

For surface area calculation, the procedure is similar. We calculate the area of the circle and add it to the square area.

The area of the 2 m side square is equal to 4 m².

Circle area of radius 1:

$\dpi{120} \mathrm{A = 3.14\cdot 1^2 = 3.14}$

Table surface area:

A = 4 + 3.14 = 7.14

Therefore, the surface area of the table is equal to 7.14 m².

You may also be interested:

Exercises on Equation of the Circumference
Difference between circumference, circle and sphere
length of circle
List of flat figure area exercises

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