Answer: The answer is (d) It is an irrational number.
Step-by-step explanation: Given formula for circumference of a circle is
![\textup{c}=\textup{r d},](https://tex.z-dn.net/?f=%5Ctextup%7Bc%7D%3D%5Ctextup%7Br%20d%7D%2C)
where 'd' is the length of the diameter and a rational number.
We are to choose one of the given four options for the circumference 'c' of the circle.
We know that the circumference of a circle with diameter 'd' is given by
![\textup{c}=\pi \textup{d},](https://tex.z-dn.net/?f=%5Ctextup%7Bc%7D%3D%5Cpi%20%5Ctextup%7Bd%7D%2C)
Comparing this with the given equation, we get
![r=\pi,~\textup{where}~\pi~\textup{is an irrational number}=\dfrac{22}{7}.](https://tex.z-dn.net/?f=r%3D%5Cpi%2C~%5Ctextup%7Bwhere%7D~%5Cpi~%5Ctextup%7Bis%20an%20irrational%20number%7D%3D%5Cdfrac%7B22%7D%7B7%7D.)
Now, the product of a rational and an irrational number is again irrational, so 'r × d' will be an irrational number.
Hence, the circumference, c = rd is irrational.
Thus, the correct option is (d) It is an irrational number.