Question

determine whether the realtionship between the circumference of a circle and its diameter is a direct variation. if so, identify the constant of porportionatlity. justify your response

Answer 1

So,
`C \propto d`

Therefore the constant of proportionality is
`\pi`

Explanation:

Let the radius of a circle be r

The circumference of a circle is(C)
`=2\pi r`

`=\pi d` [∵2r =d= diameter]

Therefore
`C = \pi d`

Since the value of
`\pi` is always constant. Here the diameter and the circumference are the variables.

So,
`C \propto d`

Therefore the constant of proportionality is
`\pi`