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 the area formula for a circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. We know that $A = 254.34$ in$^{2}$ and $\pi=3.14$. So, $254.34 = 3.14r^{2}$.

Step2: Solve for the radius $r$

First, divide both sides of the equation $254.34 = 3.14r^{2}$ by 3.14. We get $\frac{254.34}{3.14}=r^{2}$. So, $r^{2}=81$. Then, take the square - root of both sides. Since $r>0$, $r = 9$ in.

Step3: Calculate the diameter $d$

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

Answer:

18