Question

How do you find the diameter from the circumference of 20?

Answer 1

In this question, we are given the circumference of a circle and we have to find its diameter. To find the diameter of the circle, we will first have to find the radius of the circle. The radius of a circle is defined as the distance between the centre of the circle and any point lying on the boundary of the circle. Circumference of a circle is equal to twice the product of $\pi$ and the radius of the circle. From this formula we can find the radius of the circle and then its diameter.

Complete step-by-step solution:
We are given that the circumference of the circle is 20 units.
We know that the circumference of a circle is $2\pi r$ .
So, we get –
$2\pi r = 20 \\\ \Rightarrow r = \dfrac{{20}}{{2\pi }} \\\$
Now, we know that the diameter is defined as the length of line segment passing through the centre of the circle while joining two points on the circle, so the diameter is twice the length of the radius.
$d = 2r \\\ \Rightarrow d = 2 \times \dfrac{{20}}{{2\pi }} \\\ \Rightarrow d = \dfrac{{20}}{\pi } = 6.366 \\\$
Hence, the diameter of the circle having circumference 20 units is equal to $\dfrac{{20}}{\pi }$ or $6.366$ units.

Note: Circumference, also known as the perimeter of the circle, is equal to the length of the boundary of the circle. We know that the diameter $= 2r$ and circumference $= 2\pi r$ , so on dividing the circumference by diameter we get $\pi$ as the answer, that is, the ratio of the circumference of the circle and its diameter is equal to $\pi$ . Thus, the question can also be solved by using this relation.