Math Doubts

Constant property of a circle

The ratio of a circle’s circumference and its diameter is always a constant.

Introduction

To start studying the circles in geometry, everyone must learn an important property firstly. The ratio of the circumference of a circle to its diameter is a constant. It can be observed by comparing the ratios of two different circles. So, let’s construct two circles with different radii geometrically.

From a point, turn the thread around circle to reach the same point. After that, cut the thread and compare the length of the thread by a ruler. Remember, the length of the thread is the circumference of that circle.

constant property of circle

You will observe that the length of the thread is equal to the $18.85 \,cm$ approximately. We know that the radius of the circle is $3 \,cm$. So, the diameter of the circle is equal to $6 \,cm$. Now, find their ratio mathematically.

$Ratio$ $\,=\,$ $\dfrac{18.85}{6}$

$\implies$ $Ratio$ $\,=\,$ $\dfrac{\cancel{18.85}}{\cancel{6}}$

$\implies$ $Ratio$ $\,=\,$ $3.1416666666\cdots$

$\,\,\,\therefore\,\,\,\,\,\,$ $Ratio$ $\,\approx\,$ $3.1417$

Repeat the same procedure for drawing another circle geometrically and calculate the ratio.

constant property of circle

In this case, the radius of the circle is $4\,cm$. So, its diameter is equal to $8\,cm$. You will observe that the circumference of the circle is $25.15\,cm$ approximately. Now, calculate the ratio of the circle’s circumference to its diameter.

$Ratio$ $\,=\,$ $\dfrac{25.15}{8}$

$\implies$ $Ratio$ $\,=\,$ $\dfrac{\cancel{25.15}}{\cancel{8}}$

$\implies$ $Ratio$ $\,=\,$ $3.14375$

$\,\,\,\therefore\,\,\,\,\,\,$ $Ratio$ $\,\approx\,$ $3.1437$

Property

Compare the ratios for understanding the constant relation between the circumference of a circle to its diameter.

  1. In the case of $3\,cm$ radius circle, the ratio of circle’s circumference and its diameter is $3.1417$
  2. In the case of $4\,cm$ radius circle, the ratio of circle’s circumference and its diameter is $3.1437$

The two ratios are approximately equal. Even, you construct another circle with a different radius, you get the same value because the ratio of the circumference of a circle to its diameter is always constant. It is called the constant property of a circle.

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved