Question

if a circular railroad crossing sign has an area of 254.34 in.², what is the diameter of the sign? use 3.14 for π. type a number in the box. in.

Explanation:

Step1: Recall circle - area formula

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Given $A = 254.34$ in² and $\pi=3.14$. We can solve for $r$.
$254.34=3.14r^{2}$

Step2: Solve for $r^{2}$

Divide both sides of the equation by 3.14:
$r^{2}=\frac{254.34}{3.14}=81$

Step3: Solve for $r$

Take the square - root of both sides. Since $r>0$ (radius is a non - negative quantity), $r = \sqrt{81}=9$ in.

Step4: Find the diameter $d$

The diameter $d$ of a circle is related to the radius by $d = 2r$. Substitute $r = 9$ in into the formula:
$d=2\times9 = 18$ in.

Answer:

18