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 of 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 \( A = 254.34\) \( \text{in}^2 \) and \( \pi=3.14 \). First, we can solve for \( r^{2} \) by rearranging the formula: \( r^{2}=\frac{A}{\pi} \).
Substitute the given values: \( r^{2}=\frac{254.34}{3.14} \)
Calculate \( \frac{254.34}{3.14}=81 \). So \( r^{2} = 81 \).

Step2: Solve for the radius \( r \)

Since \( r^{2}=81 \), we take the square root of both sides. \( r=\sqrt{81}=9 \) inches (we take the positive root because radius is a positive quantity).

Step3: Find the diameter \( d \)

The diameter of a circle is related to the radius by the formula \( d = 2r \). Substitute \( r = 9 \) into the formula: \( d=2\times9 = 18 \) inches.

Answer:

18