The friction exerted by the fluid on an object depends on the shape of the object, speed of the object and nature of the fluid.
If the object is broad, it gives more area for the friction to act on. Thus, a streamlined body structure helps to cut through the fluid and reduce friction.
The speed of the object moving through a fluid affects the amount of friction acting against the motion of the object. More the speed, more is the friction.
The nature of the fluid also affects friction. More dense the fluid, more the friction it offers.
The volume of the fluid has no effect on the friction offered by it.