Question

What is the circumference of a circle when the diameter is $18?$

Answer 1

Hint: The circumference of a circle is the length of the boundary of the circle. We can find the circumference of a circle when the radius is given using the formula $c=2\pi r$ where $r$ is the radius. The radius of a circle is the half of the diameter of the circle.

Complete step by step solution:
Let us consider the given problem.
We are asked to find the circumference of a circle. The diameter of the circle is given. And it is $18.$
We are familiar with the formula that is used for finding the circumference of a circle when the radius is given.
If the radius of a circle is $r$ units, then the circumference of the circle is obtained by the formula $c=2\pi r.$ We can interpret this as the circumference of the circle is $2\pi r$ units.
Let us use this formula to find the circumference of the circle with diameter $18.$
We know that we need to know the radius of the circle in order to find the circumference.
In the given problem, we are given the diameter of the circle instead of the radius.
We know that the radius of a circle is half of the diameter.
So, if the radius is $r$ units, then the diameter is $2r$ units.
From this, we can say that the radius can be obtained by dividing the diameter by $2.$
Therefore, we will obtain the radius as $r=\dfrac{18}{2}=9.$
Thus, the circumference of the circle is $c=2\pi r=2\times 9\times \pi =18\pi .$

Note: The value of $\pi =3.141.$ Remember that the length of the line joining the center of a circle with any point in the boundary of the circle is called the radius of the circle. Similarly, the length of the line joining any two points in the boundary of the circle and that passes through the circle is called the diameter of the circle.