Question

where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?

Answer 1

The circumference is a irrational number

Explanation:

we know that

The circumference of a circle is equal to

`C=\pi D`

where

D is the diameter

In this problem we have that

`D=d\ units` ---> is a rational number

substitute

`C=\pi (d)`

`C=d\pi\ units`

Remember that

The number π is a irrational number

and

If you multiply a rational number by a irrational number, the result is a irrational number

therefore

The circumference is a irrational number