The surface area of a right circular cylinder is calculated using the formula:
Surface Area = 2πr² + 2πrh
In this case, we are given the surface area as 715.92 meters² and the diameter of the circle attached to the rectangle is 12 meters. The radius (r) would be half of the diameter = 6 meters.
So, let's plug in the values to the formula and solve for the height (h):
715.92 = 2 * 3.14 * 6² + 2 * 3.14 * 6h
715.92 = 226.08 + 37.68h
489.84 = 37.68h
h = 489.84 / 37.68
h = 13 meters
Therefore, the height of the rectangle is 13 meters.