Question

If a circle has the circumference of \[10 \pi\] . What is the circle’s diameter?

Answer 1

Hint: In this question, we need to seek out the diameter of the circle. Given that the circle has the circumference of \[10\pi\] . Here pie is nothing but a mathematical constant \[\pi\] . To find the diameter of the circle , we can use the formula of circumference of a circle . The formula of the circumference is given by \[2\pi r\] , where \[r\] is the radius of the circle. As given in the question the circumference of a circle is \[10\pi\] , so equating this value to the formula of the Circumference which is \[2\pi r\] . Thus we obtain the radius of the circle. From the radius of the circle, we can find the diameter of the circle by multiplying the radius by \[2\] .

Complete step-by-step answer:
Given , the circumference of the circle is \[10\pi\] .
Here we need to find the diameter of the circle.
First let us find the radius of the circle from which we can find the diameter of the circle. Since the radius of the circle is half of its diameter .
We know that the circumference of the circle is \[2\pi r\] .
In question, given that the circumference of the circle is \[10\pi\] .
So by equating \[2\pi r\] and \[10\pi\] ,
We get,
\[2\pi r = 10\pi\]
On simplifying,
We get,
\[\Rightarrow \ r = \dfrac{10}{2}\]
On dividing,
We get,
\[\Rightarrow \ r = 5\]
So the radius of the circle is \[5\] units.
Now we need to seek out the diameter of the circle.
We know that the radius of the circle is half of its diameter .
\[\Rightarrow \ r = \dfrac{d}{2}\]
On rearranging ,
We get,
\[\Rightarrow \ d = 2r\]
By substituting the value of \[r\],
We get,
\[d = 2 \times 5\]
On simplifying,
We get,
\[\Rightarrow \ d = 10\]
Thus we get the diameter of the circle is \[10\] units.
Final answer :
The diameter of the circle is \[10\] units.

Note: Mathematically, in a circle when a line a drawn from the centre to any point on the circle then that line is known as the radius of the circle similarly when a line is drawn from a end point to the other end point of the circle passing through the centre of the circle is known as diameter of a circle. Also, The ratio of circumference of the circle to its diameter is constant \[\pi\] which can be written as
\[\dfrac{\text{Circumference}}{\text{diameter}} = \pi\]
So, using this relation also, we can directly find the diameter of the circle.