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 \( A = 254.34\) and \( \pi=3.14 \), so we can 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 length, \( r = \sqrt{81}=9 \) inches.

Step4: Find the diameter

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

Answer:

18