Question

the area of a circle is 25π square miles. what is the diameter?
a = 25π mi²
give the exact answer in simplest form.
miles

Explanation:

Step1: Use the area formula of a circle

The area formula of a circle is \(A = \pi r^{2}\). Given \(A = 25\pi\), we have \(\pi r^{2}=25\pi\). Divide both sides by \(\pi\): \(r^{2}=25\).

Step2: Solve for the radius

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = 5\) (because \(\sqrt{25}=5\)).

Step3: Calculate the diameter

The diameter \(d\) of a circle is related to the radius \(r\) by the formula \(d = 2r\). Substitute \(r = 5\) into the formula: \(d=2\times5\).

Answer:

\(10\)