Question

the area of a circle is 64π square feet. what is the diameter? give the exact answer in simplest form. feet submit

Explanation:

Step1: Recall 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. Given \(A = 64\pi\), we substitute into the formula: \(\pi r^{2}=64\pi\).

Step2: Solve for the radius \(r\)

Divide both sides of the equation \(\pi r^{2}=64\pi\) by \(\pi\): \(r^{2}=\frac{64\pi}{\pi}=64\). Then take the square - root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = \sqrt{64}=8\).

Step3: Calculate the diameter \(d\)

The relationship between the diameter \(d\) and the radius \(r\) of a circle is \(d = 2r\). Substitute \(r = 8\) into the formula: \(d=2\times8 = 16\).

Answer:

16