Circumference is found in everyday life, at least, than a rectangle. And for many people, the problem of how to calculate the length of a circle is difficult. And all because she has no corners. With their presence, everything would be much easier.
What is a circle and where does it occur?
This flat figure represents a number of points that are located at the same distance from another one, which is the center. This distance is called the radius.
In everyday life, it is not often necessary to calculate the length of a circle, except for people who are engineers and designers. They create designs of mechanisms that use, for example, gears, portholes and wheels. Architects create houses that have round or arched windows.
Each of these and other cases requires its own accuracy. Moreover, it is absolutely impossible to calculate the circumference length. This is due to the infinity of the base number that is in the formula. "Pi" is still being clarified. And most often used rounded value. The degree of accuracy is chosen such as to give the most correct answer.
Designation of quantities and formulas
Before calculating the length of the circle, you need to agree on what letter means. It is convenient to write in the table.
Now it is easy to answer the question of how to calculate the circumference of a circle along a radius; this will require the following formula:
Hereinafterπ is taken rounded. Most often, tasks use the value 3.14. But sometimes greater accuracy is needed and then such a number is used: 3.14159.
Since the radius and diameter are related to each other, there is another formula for calculations. Since the radius is two times smaller, the expression will change a bit. And the formula of how to calculate the circumference, knowing the diameter, will be as follows:
What if you need to calculate the perimeter of the circle?
Just remember that the circle includes all the points inside the circle. So, its perimeter coincides with its length. And after calculating the circumference, put an equal sign with the perimeter of the circle.
By the way, they have the same designations. This applies to the radius and diameter, and the perimeter is the Latin letter P.
Examples of tasks
Condition. Find out the length of a circle whose radius is 5 cm.
Decision. It is easy to understand how to calculate the length of the circle. You only need to use the first formula. Since the radius is known, you only need to substitute the values and count. 2 multiplied by a radius of 5 cm will give 10. It remains to multiply it by the value π. 3.14 * 10 = 31.4 (cm).
Condition. There is a wheel, the circumference of which is known and is equal to 1256 mm. It is necessary to calculate its radius.
Decision. In this task you will need to use the same formula. But only the known length will need to be divided into the product of 2 and π. It turns out that the product will give the result: 6.28. After division, the number remains: 200. This is the desired value.
Condition. Calculate the diameter if the circumference is known, which is 56.52 cm.
Decision. Similarly to the previous task, you will need to divide the known length by the π value, rounded to hundredths. As a result of this action, the number 18 is obtained. The result is obtained.
Condition. The hands of the clock have a length of 3 and 5 cm. It is necessary to calculate the length of the circles that describe their ends.
Decision. Since the arrows coincide with the radii of the circles, we need the first formula. She needs to use it twice.
For the first length, the product will consist of multipliers: 2; 3.14 and 3. The result will be the number of 18.84 cm.
For the second answer you need to multiply 2, π and 5. The product will give the number: 31.4 cm.
Condition. A squirrel runs in a wheel with a diameter of 2 m. What distance does it run in one full revolution of the wheel?
Decision. This distance is equal to the circumference. Therefore, you need to use the appropriate formula. Namely, multiply the value of π and 2 m. Calculations give the result: 6.28 m.
Answer: The squirrel runs 6.28 m.