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. We know $A = 254.34$ in.$^{2}$ and $\pi=3.14$.

Step2: Solve for radius $r$

Substitute values into the formula: $254.34=3.14r^{2}$. Then $r^{2}=\frac{254.34}{3.14}=81$. Taking the square - root of both sides, $r = 9$ in (we take the positive value since radius is non - negative).

Step3: Calculate the diameter $d$

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

Answer:

18