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.

Explanation:

Step1: Recall area formula of circle

The area \( A \) of a circle is given by the formula \( A=\pi r^{2} \), where \( r \) is the radius of the circle. We know \( A = 254.34\) \( \text{in}^2 \) and \( \pi=3.14 \). So we can substitute these values into the formula to find the radius first.
Substituting the values, we get \( 254.34=3.14\times r^{2} \).

Step2: Solve for radius \( r \)

First, divide both sides of the equation \( 254.34 = 3.14\times r^{2} \) by \( 3.14 \).
\( r^{2}=\frac{254.34}{3.14} \)
Calculating \( \frac{254.34}{3.14} \), we get \( r^{2} = 81 \).
Then, take the square root of both sides. Since the radius is a positive quantity, \( r=\sqrt{81}=9 \) inches.

Step3: Find the diameter \( d \)

The diameter \( d \) of a circle is related to the radius \( r \) by the formula \( d = 2r \).
We found that \( r = 9 \) inches, so substituting \( r = 9 \) into the formula for diameter, we get \( d=2\times9 = 18 \) inches.

Answer:

18