It's not possible to determine the volume of the roof using trigonometry alone, as trigonometry deals with angles and side lengths of triangles, not volumes of objects.
To find the volume of the roof, we would need additional information about the shape of the roof, such as its height, width, and length. Once we have that information, we could use geometry or calculus to calculate the volume of the roof.
(Please list the given information to the problem, as it is currently impossible.)