Question

1. you are finding the area of a circle with a radius of 2 feet. is the area a rational or irrational number? explain.

Explanation:

Step1: Recall circle area formula

The area of a circle is given by $A = \pi r^2$, where $r$ is the radius.

Step2: Substitute radius value

Substitute $r = 2$ feet into the formula:
$A = \pi (2)^2 = 4\pi$

Step3: Classify the number

$\pi$ is an irrational number. The product of a non-zero rational number (4) and an irrational number ($\pi$) is irrational.

Answer:

The area of the circle is $4\pi$ square feet, which is an irrational number. This is because $\pi$ is irrational, and multiplying it by the rational number 4 results in an irrational number (a non-repeating, non-terminating decimal).