Question

the area of a circle is 254.34 square feet. what is the circles diameter? round your answer to the nearest hundredth. feet

Explanation:

Step1: Use 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. Given \(A = 254.34\) square feet and \(\pi\approx3.14\). Then \(254.34=3.14r^{2}\).

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

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

Step3: Solve for \(r\)

Take the square - root of both sides. Since \(r>0\), \(r=\sqrt{81}=9\) feet.

Step4: Calculate the diameter \(d\)

The diameter \(d = 2r\). Substitute \(r = 9\) into the formula, \(d=2\times9 = 18.00\) feet.

Answer:

\(18.00\)