Question

1. a circular dartboard has a radius of 10 inches. what is the area of the dartboard using a = πr²? is the result rational or irrational?

Explanation:

Step1: Recall area formula for circle

The area formula of a circle is $A = \pi r^{2}$, where $r$ is the radius.

Step2: Substitute given radius

Given $r = 10$ inches, we substitute into the formula: $A=\pi\times(10)^{2}=100\pi$ square - inches. Since $\pi$ is an irrational number, the area $100\pi$ is also irrational.

Answer:

The area of the dart - board is $100\pi$ square inches and it is irrational.