Question

the area of a circle is 25π square inches. find the diameter of the circle.

Explanation:

Step1: Recall area formula

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Given $A = 25\pi$.

Step2: Solve for radius

Set $\pi r^{2}=25\pi$. Divide both sides by $\pi$: $r^{2}=25$. Taking the square - root of both sides, we get $r = 5$ (we consider the positive value since radius is non - negative).

Step3: Find the diameter

The diameter $d$ of a circle is related to the radius by $d = 2r$. Substitute $r = 5$ into the formula, so $d=2\times5 = 10$ inches.

Answer:

10 inches