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 \( \pi=3.14 \). Substitute these values into the formula:
\( 254.34 = 3.14\times r^{2} \)

Step2: Solve for \( r^{2} \)

Divide both sides of the equation by \( 3.14 \):
\( r^{2}=\frac{254.34}{3.14} = 81 \)

Step3: Solve for \( r \)

Take the square root of both sides. Since the radius is a positive quantity, we have:
\( r=\sqrt{81}=9 \) \( \text{in} \)

Step4: Find the diameter

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

Answer:

18