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 area formula for circle

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

Step2: Solve for radius $r$

Divide both sides of the equation by $3.14$:
$\frac{254.34}{3.14}=r^{2}$
$r^{2}=81$
Take the square - root of both sides: $r = 9$ in. (we take the positive value since radius is a non - negative quantity).

Step3: Calculate the diameter $d$

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

Answer:

18