Circumference is found in everyday life no less than a rectangle. And for many people the problem of how to calculate the circumference of a circle causes difficulty. And all because she does not have corners. If they were available, everything would be much easier.
What is a circle and where does it meet?
This flat figure represents a number of points that are located at an equal distance from another, which is the center. This distance is called the radius.
In everyday life, it is not often necessary to calculate the circumference of a circle, except for people who are engineers and designers. They create drafts of mechanisms in which, for example, gears, portholes and wheels are used. Architects create houses with round or arched windows.
Each of these and other cases requires its own accuracy. And it is impossible to calculate the circumference accurately. This is due to the infinity of the basic number in the formula. "Pi" is still being specified. And the most often rounded value is used. The degree of accuracy is chosen to give the most correct answer.
Notation of quantities and formulas
Before calculating the length of the circle, it will be necessary to agree on what letter that stands for. 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 in radius, this requires the following formula:
Here and belowπ is taken rounded. Most often, the task uses the value 3.14. But sometimes more precision is needed and then a number is used: 3.14159.
Since the radius and diameter are related to each other, that is, another formula for calculations. Since the radius is half the size, the expression will slightly change. And the formula of how to calculate the circumference of a circle, knowing the diameter, will be as follows:
What if I need to calculate the perimeter of a circle?
Just remember that the circle includes all the points inside the circle. So, its perimeter coincides with its length. And after calculating the length of the circle, put an equal sign with the perimeter of the circle.
By the way, they have the same designations. This concerns the radius and diameter, and the perimeter is the Latin letter P.
Examples of tasks
Condition. Find the length of a circle whose radius is 5 cm.
Decision. Here it is easy to understand how to calculate the circumference of a circle. We need only use the first formula. Since the radius is known, you only need to substitute the values and count them. 2 multiplied by a radius of 5 cm gives 10. It remains to multiply it by the value of π. 3.14 * 10 = 31.4 (cm).
Condition. There is a wheel whose circumference is known and 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 a known length will need to be divided into product 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 equal to 56.52 cm.
Decision. Similar to the previous problem, you need to divide the known length by the value of π, rounded to the nearest hundredth. 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. We need to calculate the lengths of the circles that describe their ends.
Decision. Since the arrows coincide with the radii of the circles, the first formula is required. It needs to be used twice.
For the first length, the product will consist of multipliers: 2; 3.14 and 3. The result is the number 18.84 cm.
For the second answer, multiply 2, π, and 5. Multiply the product by 31.4 cm.
Condition. The squirrel runs in a wheel 2 m in diameter. What distance does it run for one full turn of the wheel?
Decision. This distance is equal to the length of the circle. Therefore, we need to use a suitable formula. Namely, multiply the value of π and 2 m. Calculations give the result: 6.28 m.
Answer: The squirrel runs 6.28 m.