Car Talk Question: Height of fill line of cylindrical gas tank

Question

I remember hearing about this question from Car Talk and don't remember how to find the answer.

The gas tank on a truck is a horizontal cylinder. A driver wants to mark the circular face of the tank where the tank is one-quarter full. Half is easy because it's halfway across the circle, but how high up is the one-quarter full fill line? Radius=R.

Answer 1

Deteremine the segment that is 0.25 the area of the cirular side.

Answer 2

The best method IRL would be to find the total volume of the tank, quarter it, put that much gas in the tank, and mark the fill line from there, but that's the practical way, not the math way!