Question

If $C$ is the circumference of a circle of radius $r$ , then which of the following statements is true?
A. $\dfrac{C}{r}<6$
B. $\dfrac{C}{r}=6$
C. $\dfrac{C}{r}>6$
D. $\dfrac{C}{r}=\pi $

Answer 1

Hint: Here we have to find which of the given options is correct for a circle with circumference $C$ and radius $r$ . Firstly we will write the formula for finding the circumference of the circle. Then we will find the value of the fraction of circumference to radius as shown in our options and see which among the given options is correct. Use $\pi =\dfrac{22}{7}$

Complete step-by-step answer:
The information about the circle is given as follows:
Circumference $=C$…$\left( 1 \right)$
Radius $=r$….$\left( 2 \right)$
We can draw the circle with above values as follows:

We know the formula of circumference is as follows:
Circumference $=2\pi \times $ Radius
Substitute the values from equation (1) and (2) above we get,
$\Rightarrow C=2\pi \times r$
Now take the radius value on the left side as follows:
$\Rightarrow \dfrac{C}{r}=2\pi $
We know $\pi =\dfrac{22}{7}$ on substituting the value above we get,
$\Rightarrow \dfrac{C}{r}=2\times \dfrac{22}{7}$
$\Rightarrow \dfrac{C}{r}=6.286$
As $6.286>6$
$\therefore \dfrac{C}{r}>6$
So we get that the fraction of circumference to radius is greater than $6$
So, the correct answer is “Option C”.

Note: Circle is a two-dimensional closed figure in which the set of all the points is equidistant from a middle point known as center. The longest line or chord that we can make inside a circle is known as its diameter and half the value of diameter is known as the radius. The diameter of the circle divides the circle into two parts. The circumference is the length of the circular shape of the circle. Circumference is also known as the perimeter but perimeter is usually used for the figures made up of the straight line segment. We can take $\pi =3.14$ also and still get the same condition.