Question

What is the diameter in inches of a circle that has an area of 16pi square inches

Answer 1

Area of a circle = pi * r^2
16pi=pi * r^2
Divide both sides by pi
16=r^2
Square root both sides
4=r
Diameter=2r=2*4=8 inches

Answer 2

$\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=16\pi \end{cases}\implies 16\pi =\pi r^2\implies \cfrac{16\pi }{\pi }=r^2\implies 16=r^2 \\\\\\ \sqrt{16}=r\implies 4=r~\hfill \stackrel{\textit{diameter is twice the radius}}{d=8}$