Question

what is the radius of a circle if the area is 254.5 in²?

Explanation:

Step1: Write the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(A\) is the area and \(r\) is the radius.

Step2: Substitute the given area into the formula

Given \(A = 254.5\space in^{2}\) and taking \(\pi\approx3.1416\), we have \(254.5=3.1416r^{2}\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation by \(3.1416\): \(r^{2}=\frac{254.5}{3.1416}\approx81\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r=\sqrt{81} = 9\space in\).

Answer:

The radius of the circle is \(9\space in\).