sat-dog

Choice B is correct. The standard form of an equation of a circle in the xy-plane is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$, where the coordinates of the center of the circle are $\left(h,k\right)$ and the length of the radius of the circle is $r$. For the circle in the xy-plane with equation ${\left(x-5\right)}^2+{\left(y-3\right)}^2=16$, it follows that $r^2=16$. Taking the square root of both sides of this equation yields $r=4$ or $r=-4$. Because $r$ represents the length of the radius of the circle and this length must be positive, $r=4$. Therefore, the radius of the circle is $4$. The diameter of a circle is twice the length of the radius of the circle. Thus, $2\left(4\right)$ yields $8$. Therefore, the diameter of the circle is $8$.

Choice A is incorrect. This is the radius of the circle. 

Choice C is incorrect. This is the square of the radius of the circle. 

Choice D is incorrect and may result from conceptual or calculation errors.