Diameter of a circle is defined as the longest chord or line joining the two points of a circle but most important point is that it shall pass through the center of circle. In a circle there can be infinite number of diameters. Its relation with radius is that it is twice the radius of circle. It is also useful in calculating area and circumference of circle by the following formulas:-
Circumference of circle = pie * d
Area of circle = pie * (d/2) ^2
This can be more clarified by taking some suitable examples.
Problem 1: Find the diameter of circle by first finding the radius of circle when circumference of circle is 44/7cm.
Solution: Given Circumference of circle = 44/7 cm and Let r is radius of circle.
=> We know that in terms of radius, the circumference of circle = 2* pie*r
=> Therefore, 44/7 = 2 * 22/7 * r
=> So r = (44/7)/ 44/7 = 1 cm
=> Hence diameter of circle = 2* r = 2* 1 = 2 cm.
Problem 2: Find the diameter by Pie* diameter formula if the Circumference of the circle is 2200.
Solution: Given Circumference of the circle = 2200 cm
=> By Pie* diameter formula of circumference,
=> We have, Circumference of circle = Pie*diameter
=> 2200 = 22/7 * diameter
=> Therefore, diameter = 2200 *7 /22 = 100* 7 = 700 cm
=> Therefore the diameter of the circle is 700 cm.