Question

The formula for the circumference of a circle is c=rd, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference? It is a fraction. It is a repeating or terminating decimal. It is a rational number. It is an irrational number.

Answer 1

The statement that is true about the circumference of the circle is:

• It is an irrational number.

Explanation:

The formula for the circumference of a circle is :

c=πd where d is the length of the diameter.

and π is a irrational number.

If d is a rational number, then as we know that the multiplication of a rational and a irrational number is always irrational.

Hence, the value of circumference is an irrational number.

Answer 2

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},`

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},`

Comparing this with the given equation, we get

`r=\pi,~\textup{where}~\pi~\textup{is an irrational number}=(22)/(7).`

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.