if a circular railroad crossing sign has an area of 254.34 in.², what is the diameter of the sign? use 3.14…

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.

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.

Answer

Explanation:

Step1: Recall area - radius 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 $r$ by rearranging the formula: $r^{2}=\frac{A}{\pi}$.

Step2: Calculate the radius squared

Substitute the values into the formula: $r^{2}=\frac{254.34}{3.14}=81$.

Step3: Find the radius

Take the square - root of both sides. Since $r^{2}=81$, then $r = 9$ in (we take the positive value because radius is a non - negative quantity).

Step4: Calculate the diameter

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

Answer:

18