How to determine the radius of a circle, knowing its length
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Video: Finding Radius Given Arc Length and Angle Measure 2024, July
The radius is usually known in geometric problems, and the circumference must be calculated. But the opposite situation may arise when, for a given circumference, it is necessary to determine how far it will be from the center, that is, to calculate the radius.
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According to the sixth grade curriculum, students of secondary schools in the course of geometry study the circle and circle as a geometric figure, and everything connected with this figure. Children get acquainted with such concepts as radius and diameter, circumference or circle perimeter, circle area. It is on this topic that they learn about the mysterious Pi number - this is the Ludolph number, as it was called before. The number Pi is irrational, since its representation as a decimal is infinite. In practice, its truncated version of three digits is used: 3.14. This constant expresses the ratio of the length of any circle to its diameter.
Sixth-graders solve problems, deriving the other characteristics of a circle and a circle, given one given and the number Pi. In notebooks and on the chalkboard, they draw abstract spheres on a scale and perform little speaking calculations.
But in practice
In practice, such a task can arise in a situation where, for example, there is a need to lay a route of a certain length to conduct any competitions with a start and finish in one place. Having calculated the radius, you will be able to choose the passage of this route on the plan, with a compass in your hand, considering options taking into account the geographical features of the region. By moving the leg of the compass - an equidistant center from the future route, it is already possible at this stage to foresee where there will be ascents on the plots, where there are descents, taking into account the natural changes in the relief. You can also immediately determine the areas where it is better to place stands for fans.
Circle radius
So, suppose you need a 10, 000 m long circular track to run an autocross competition. Here is the formula you need to determine the radius (R) of a circle with its known length (C):
R = C / 2n (n is a number equal to 3.14).
Substituting the available values, you easily get the result: