Cardinal 177/177RG
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 143; Flight Crew Total 1225; Flight Crew Type 100
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Fuel Issue
Air Traffic Control Provided Assistance; Flight Crew Landed in Emergency Condition
Human Factors; Procedure
This my recollection of the events of date that resulted in the landing at ZZZ.That morning; I met Name; a private pilot to whom I am providing instrument instruction; at ZZZ1 airport. When I arrived; Name had already conducted a preflight inspection of Aircraft X. Unfortunately; I did not verify the fuel quantity in the aircraft and relied on Name to do so. The plan for this flight was the do the RNAV XX Approach into ZZZ2; go missed; and then fly VFR back to ZZZ1.After the missed approach at ZZZ2 and upon reaching 3;500 ft.; the engine quit without warning. I took control of the airplane; requested priority  with ZZZ2 Approach; and turned towards ZZZ. I was cleared for the runway and landed on Runway XYR without further incident. We could not restart the plane in the air or the ground. There is some background needed at this point. Prior to this flight; I was the last person to fly this plane. As part of our standard practice; after the last flight I requested fuel service from the FBO and asked that the plane be put away for the night. Assuming the FBO would honor my request; I left for the evening. When I arrived at the airport; Name had completed the preflight and confirmed there was fuel in the aircraft. I've flown with Name many times and found him to be a very competent pilot. Also; I have never had the FBO fail to fill the plane. Accordingly; I did not have reason to think there was not enough fuel in the aircraft. When we started the plane; we reset the fuel totalizer for full fuel; so when the engine quit; I expected there to be nearly 40 gallons of fuel in the plane when it was indeed empty.There are several lessons to learn here. As an instructor you can never fully trust your student; even if a certificated pilot; and it's important to verify all information. Another factor was expectation bias--as part of our standard practice; the aircraft is always put away with full fuel and the FBO has never failed to honor this request. When I arrived at the airport; I expected the aircraft to have full fuel and expected my student to verify this for me. Another factor is that it is impossible to view the fuel gauges from the right seat on the Cessna cardinal as they are on the left of the pilot side yoke; so I was unable to use them to verify the fuel state. In order to prevent a recurrence; I am going to suggest to the club that we standardized a way to measure the fuel and to make it a requirement to measure fuel before every flight. The aircraft's fuel quantity is difficult to check visually since there is a spring-loaded cover over the fuel port. At the end of the day; however; I was the flight instructor and should have verified the fuel quantity before departing.
Flight instructor reported they thought another pilot or the FBO had filled the aircraft with fuel.  Engine quit due to fuel starvation.