Maintaining straight and level altitude just a completely random question that I suddenly thought - doesn't straight and level flight prove that the earth's surface is not a globe? Once cruising altitude is reached, the plane remains at the same altitude for the entire flight until it starts to descend for landing. If earth was a globe, we would need to drop the nose of the plane every couple of minutes to compensate for the curve of the earth. Is this correct? Because on my most recent flight, we reached 2000ft altitude and my instructor told me to maintain this altitude for 30 minutes (which I managed to do). I asked why we don't need to compensate for the curve of the earth and he couldn't answer me. Sorry for the random question but it's been bothering me.
Set aside the barometric stuff.  The simple answer is that what we think of as altitude, on a sphere, is really distance from the gravitational source, the center of the sphere.  Therefore, a "constant altitude" is not maintaining the same plane in 3 dimensional space, but the same distance from the center of the earth.