The formula to calculate the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Plugging in the values:
V = 3.14 * (5.9)^2 * 15.6
V = 3.14 * 34.81 * 15.6
V = 3.14 * 543.336
V = 1706.4864 cubic inches
Rounded to the nearest tenth: V = 1706.5 cubic inches
Therefore, the volume of the paint bucket is 1706.5 cubic inches.