It looks from your calculations that you have a circular region around the tree with a radius of 36 inches (1 yard) and you want to put 6 inches of mulch in this region. The area of this region is then
r2 = 3.14 362 = 4069.44 square inches.
If you had used the radius in yards (1 yard) then the area calculation would be
r2 = 3.14 12 = 3.14 square yards.
To find the volume of mulch you need to multiply by the thickness (again in yards). There are 36 inches in a yard so
6 inches = 6/36 = 1/6 yards.
Thus the volume of mulch you need is
3.14 1/6 = 0.523 cubic yards
or approximately one half a cubic yard.