Question

If the circumference of a circle is \[25\] cm, What is its diameter?

Answer 1

Hint: We use the concepts which will define a circle. And we will learn about the terminologies like radius, diameter and circumference and we will look at them with detailed explanation. We use some transposition techniques also to solve this problem.
A circle is a polygon with infinite sides.

Complete step by step solution:
In mathematics, a circle is a 2-Dimensional figure which is defined as the locus of points on a plane which are equidistant to a given point.
And the given point is called the Centre of the circle and the distance from centre to any other point on locus is called Radius of circle.

The length of line joining opposite points on a circle passing through the centre is called the Diameter and we can conclude that, Diameter is equal to twice the Radius. And it is denoted by ‘\[d\]’.
The perimeter of a circle is called as Circumference of the circle.
When we divide the Circumference of a circle by its diameter, then we get a constant value which is \[{\text{3}}{\text{.1415}}\] and this constant is denoted by \[\pi {\text{ = 3}}{\text{.1415}}\]
So, in mathematical form, we can write this as,
\[ \Rightarrow \dfrac{{{\text{circumference}}}}{{{\text{diameter}}}} = \pi \]
So, on cross multiplying, we get,
\[ \Rightarrow {\text{circumference}} = \pi \times d\]
We know that diameter is twice the radius.
\[ \Rightarrow {\text{circumference}} = \pi \times 2r\]
So, we can conclude that, \[{\text{Circumference}} = 2\pi r\]
Now in the question, it is given that the circumference is equal to \[25{\text{ cm}}\].
So, we will write it as,
\[{\text{Circumference}} = \pi \times d = 25{\text{ cm}}\]
Simply, \[\pi \times d = 25\]
Dividing this whole equation by \[\pi \], we get, \[d = \dfrac{{25}}{\pi }\]
\[ \Rightarrow d = \dfrac{{25}}{{3.14}} = 7.96{\text{ cm}}\]
Therefore, the diameter of a circle with circumference \[25{\text{ cm}}\] is \[7.96{\text{ cm}}\].

Note:
The value \[\pi \] is an irrational number. That means it is a non-terminating non-repeating decimal number. And its value is \[\pi = 3.1415926.....\]
But still, it can be written in fraction form as a rational number as \[\pi = \dfrac{{22}}{7}\].
 And this value has no units.