Question

The ratio of the circumference of a circle to twice the diameter of the circle is
A. $\dfrac{\pi }{4}$
B. $\dfrac{\pi }{2}$
C. $\pi $
D. $2\pi $
E. $4\pi $

Answer 1

Hint:
We will begin by assuming the radius of a circle as $r$. Then, find the diameter which is double the radius. Circumference of a circle is given by $2\pi r$, where $r$ is the radius of the circle. Then, take the ratio of the circumference of a circle to twice the diameter of the circle.

Complete step by step solution:
We have to find the ratio of the circumference of a circle to twice the diameter of the circle.
Let the radius of the circle is $r$
We know that the diameter is double the radius of a given circle.
Then, diameter of the circle is $2r$
Circumference is the length of the boundary of the circle.
The circumference of the circle is $2\pi r$, where $r$ is the radius of the circle.
To find the ratio of the circumference of a circle to twice the diameter of the circle, we will divide circumference to the 2 the diameter of a circle.
Then,
$\dfrac{{2\pi r}}{{2\left( {2r} \right)}} = \dfrac{\pi }{2}$
Hence, the required ratio is $\dfrac{\pi }{2}$.

Thus, option B is correct.

Note:
The order of the ratio should be correct. If we want to find the ratio of the circumference of a circle to twice the diameter of the circle, then the circumference should come in numerator and the value of twice the diameter should come in denominator.