You want the total volume of a cuboid 1" × 10" × 38" and a cylinder 1" in diameter by 12" long.
Volume of a cuboid:
.. V = l*w*h
.. = (38")*(10")*(1")
.. = 380 in³
Volume of a cylinder:
.. V = (π/4)*d²*h
.. = (3.14/4)*(1")²*(12")
.. = 9.42 in³
Total volume = Volume of cuboid + Volume of cylinder
.. = 380 in³ +9.42 in³
.. = 389.42 in³
The volume of the coat rack is approximately 389.42 in³.