Rounded to the nearest integer, the volume of the cylinder is 5,878 cubic inches.
Given that the volume of a cylinder is calculated using the formula Phi x Radius ^ 2 x Height, and knowing that the cylinder in question has a height of 13 inches and a base diameter of 12 inches, to calculate said volume the following calculation must be done:
Phi x (12x12) x 13 = X
Phi x 144 x 13 = X
Phi x 1,872 = X
3.14 x 1,872 = X
5,878.08 = X
Thus, rounded to the nearest integer, the volume of the cylinder is 5,878 cubic inches.