Question

In reference to a circle, the value of $\pi $ is equal to:
A, $\dfrac{{{\text{area}}}}{{{\text{circumference}}}}$
B. $\dfrac{{{\text{area}}}}{{{\text{diameter}}}}$
C. $\dfrac{{{\text{circumference}}}}{{{\text{diameter}}}}$
D. $\dfrac{{{\text{circumference}}}}{{{\text{radius}}}}$

Answer 1

Hint:We know that the area of the circle is $\pi {r^2}$ and the circumference is $2\pi r$ and the diameter is $2r$. Here $r$ is the radius of the circle and now we need to find the value of $\pi $ in terms of area, circumference and the radius.

Complete step-by-step answer:
As we all know that the value of $\pi $ is $\dfrac{{22}}{7}$ or in the decimal system is $3.14$ and $\pi $ is used for finding the area, volume, circumference of the circle, cylinder, sphere, cone, etc.
Here we are told that in reference to the circle we need to find the value of $\pi $ and as we know that the area of the circle is given by $\pi {r^2}$ where $r$ is the radius of the circle.
Circumference of the circle is given by $2\pi r$ and diameter as $2r$ where $r$ is the radius of the circle.
Now let us consider on the following option
Option A is given as $\dfrac{{{\text{area}}}}{{{\text{circumference}}}}$
As we know that the area of the circle is given by $\pi {r^2}$ where $r$ is the radius of the circle.
Circumference of the circle is given by $2\pi r$
So we get that
$\dfrac{{{\text{area}}}}{{{\text{circumference}}}}$$ = \dfrac{{\pi {r^2}}}{{2\pi r}} = \dfrac{r}{2}$
Hence it is not equal to $\pi $
Now we see the second option which is $\dfrac{{{\text{area}}}}{{{\text{diameter}}}}$
 As we know that the area of the circle is given by $\pi {r^2}$ and diameter as $2r$ where $r$ is the radius of the circle
$\dfrac{{{\text{area}}}}{{{\text{diameter}}}}$$ = \dfrac{{\pi {r^2}}}{{2r}}$$ = \dfrac{{\pi r}}{2}$
Hence it is not equal to $\pi $
Now let us see the third option:$\dfrac{{{\text{circumference}}}}{{{\text{diameter}}}}$
Circumference of the circle is given by $2\pi r$ and diameter as $2r$ where $r$ is the radius of the circle
So $\dfrac{{{\text{circumference}}}}{{{\text{diameter}}}}$$ = \dfrac{{2\pi r}}{{2r}} = \pi $

So, the correct answer is “Option C

Note:As we know that the area of the circle is given by $\pi {r^2}$ and diameter as $2r$ where $r$ is the radius of the circle and circumference of the circle is given by $2\pi r$
Hence we can write that Circumference $ = \pi d$
$\pi = \dfrac{{{\text{circumference}}}}{{{\text{diameter}}}}$
So this would be our answer.