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# How to determine the radius of a circle, knowing its length | Education 2022

Usually, the radius is known with geometric problems and must calculate the circumference. Nevertheless, the opposite situation can also arise when it is necessary to determine how far it will be from the center for a certain perimeter, that is, to calculate the radius.

## They teach at school. They teach at school…

According to the sixth-grade curriculum, in geometry, students of public schools study the circle as a geometric figure and everything related to this figure. The boys are introduced to concepts such as radius and diameter, circumference or circumference of a circle, and circle area. On this topic, they learn about the mysterious number Pi – this is the number of Ludolph, as it was called earlier. Pi is irrational because its decimal representation is infinite. In practice, the three-digit abbreviated version is used: 3.14. This constant expresses the relationship between the length of a circle and its diameter.

Sixth-graders solve problems by deriving the other characteristics of a circle and a given circle and the number “Pi.” Then, they draw abstract spheres to scale and do small calculations in their notebooks and on the blackboard.

## But in practice

In practice, such a task can arise in a situation where, for example, it becomes necessary to construct a track of a certain length to keep a race with start and finish in one place. Having calculated the radius, you can choose the passage of this route on the plan, taking into account options with a compass in hand, taking into account the region’s geographical features. By moving the leg of the compass, the equidistant center of the future route, it is possible to foresee at this stage where there will be ups and downs in the sections, taking into account the natural differences in relief. You can also immediately determine where the stands for the fans can best be placed.

So let us say you need a 10,000-foot circular track to run an autocross race. Here is the formula you need to find the radius (R) of a circle given its length (C):

R = C / 2n (n is a number equal to 3.14).

If you replace the existing values, you can easily get the result:

R = 10,000: 3.14 = 3,184.71 (m) or 3 km 184 m and 71 cm.

## From radius to an area

Knowing the circle’s radius makes it easy to determine the area to be removed from the landscape. The formula for the area of ​​a circle (S): S = nR2

With R = 3,184.71 m, it becomes: S = 3.14 x 3,184.71 x 3,184.71 = 31,847,063 (sq. M) or nearly 32 square kilometers.

Such calculations can be helpful for fences. For example, you have material for a fence of so many running meters. Taking this value for the circumference of the circle, you can quickly determine the diameter (radius) and area, thus visually representing the size of the future fenced area. 