Question

1. lena is designing a circular mosaic. she needs to calculate the circumference using the formula c = 2πr. c = 2πr, and the radius is 6 inches. will the circumference be a rational or irrational number? why?

Explanation:

Step1: Substitute radius into formula

Given $r = 6$ inches and $C=2\pi r$, then $C = 2\pi\times6=12\pi$.

Step2: Recall the nature of $\pi$

$\pi$ is an irrational number. When an irrational number ($\pi$) is multiplied by a non - zero rational number ($12$), the result is irrational.

Answer:

The circumference is an irrational number because it is in the form $12\pi$ and $\pi$ is an irrational number.