### Instruction: Find the number of cubic centimeters in the volume of the cylinder formed by rotating a square with side length 14 centimeters about its vertical line of symmetry. Express your answer in terms of $\pi$.### Response: I know that the volume of a cylinder is given by the formula $V = \pi r^2 h$, where $r$ is the radius of the base and $h$ is the height of the cylinder.
In this case, the base of the cylinder is a circle whose diameter is equal to the side length of the square, which is 14 centimeters.
That means the radius of the base is half of that, or 7 centimeters.
The height of the cylinder is also 14 centimeters, since it is the same as the other side of the square.
Plugging these values into the formula, I get $V = \pi (7)^2 (14) = 686 \pi$ cubic centimeters.