You certainly don't need calculus, but you do need a computer or graphing calculator. If the tank has radius r, the distance from the surface of the liquid to the ground when the tank is a quarter full is r*(1 - sin(t/2)), where t is the solution to t - sin t = pi/2. There's no way to solve this equation by hand.

For an arbirtary fraction f, replace pi/2 with 2*pi*f.