A right circular cylinder has a base diameter of 22 centimeters and a height of 6

Choice C is correct. The volume, $V$, of a right circular cylinder is given by the formula $V=\pi r^{2}h$, where $r$ is the radius of the base of the cylinder and $h$ is the height of the cylinder. It's given that a right circular cylinder has a height of $6$ centimeters. Therefore, $h=6$. It's also given that the cylinder has a base diameter of $22$ centimeters. The radius of a circle is half the diameter of the circle. Since the base of a right circular cylinder is a circle, it follows that the radius of the base of the right circular cylinder is $\frac{22}{2}$, or $11$, centimeters. Therefore, $r=11$. Substituting $11$ for $r$ and $6$ for $h$ in the formula $V=\pi r^{2}h$ yields $V=\pi {\left(11\right)}^2\left(6\right)$, which is equivalent to $V=\pi \left(121\right)\left(6\right)$, or $V=726\pi$. Therefore, the volume, in cubic centimeters, of the cylinder is $726\pi$.

Choice A is incorrect. This is the volume of a right circular cylinder that has a base diameter of $2\sqrt{22}$, not $22$, centimeters and a height of $6$ centimeters.

Choice B is incorrect. This is the volume of a right circular cylinder that has a base diameter of $4\sqrt{11}$, not $22$, centimeters and a height of $6$ centimeters.

Choice D is incorrect. This is the volume of a right circular cylinder that has a base diameter of $44$, not $22$, centimeters and a height of $6$ centimeters.