Find the volume of the bottom and top separately and then add them. Cylinder volume is the area of the bottom times the height (22/7)(5^2)•175=13750 ft^3
The volume of a sphere is V=(4/3)(22/7)r^3 where r is the radius. Here that's also 5 since it fits on the cylinder. Also we only want half the sphere so use V=(2/3)(22/7)•5^3=261.9 ft^3 Which we round upto 262. Now add the parts together 13750+262=14,012 ft^3
The processes are described on the image attached below. The isobaric process consists of an horizontal line, the adiabatic expansion is described by a polytropic curve:
