Question

derive the formula for the circumference of a circle with radius r by following these steps.

1. because all circles are similar, set up a proportion of the circumference to the diameter for the two circles shown in the diagram.

\\(\frac{c_1}{d_1}=\frac{c_2}{d_2}\\)

1. suppose (d_1 = 1). by definition, what is the circumference of the smaller circle? (c_1=pi)
2. suppose the radius of the larger circle is r. what is its diameter? (d_2=)

Explanation:

Step1: Recall diameter - radius relationship

The diameter $d$ of a circle is related to the radius $r$ by the formula $d = 2r$. Given the radius of the larger circle is $r$, then its diameter $d_2=2r$.

Answer:

$2r$