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}\\) 2. suppose \\(d_1 = 1\\). by definition, what is the circumference of the smaller circle? \\(c_1 =\\) dropdown with 1, \\(\pi\\), \\(2\pi\\)

Explanation:

Step1: Recall the definition of π

The constant \( \pi \) is defined as the ratio of the circumference \( C \) of a circle to its diameter \( d \), i.e., \( \pi=\frac{C}{d} \).

Step2: Substitute \( d_1 = 1 \) into the formula

Given \( d_1 = 1 \) and using \( \pi=\frac{C_1}{d_1} \), we can solve for \( C_1 \) by multiplying both sides by \( d_1 \). So \( C_1=\pi\times d_1 \). Since \( d_1 = 1 \), then \( C_1=\pi\times1=\pi \).

Answer:

\(\pi\) (corresponding to the option with \(\pi\))