Question

the area of a circle is 50.24 square feet. what is the circles diameter? round your answer to the nearest hundredth. feet

Explanation:

Step1: Recall the area formula 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. Given \(A = 50.24\) square feet and taking \(\pi\approx3.14\).
Substitute the values into the formula: \(50.24=3.14r^{2}\).

Step2: Solve for the radius \(r\)

Divide both sides of the equation \(50.24 = 3.14r^{2}\) by \(3.14\):
\(\frac{50.24}{3.14}=r^{2}\), so \(r^{2}=16\).
Take the square - root of both sides: \(r=\sqrt{16}\), so \(r = 4\) feet.

Step3: Calculate the diameter \(d\)

The relationship between the diameter \(d\) and the radius \(r\) is \(d = 2r\).
Since \(r = 4\) feet, then \(d=2\times4\).

Answer:

\(8.00\) feet