[Ed Miller]

I'm assuming you mean that the tank is "laying on its side" rather than standing on its base (or else 5 inches would be the answer).

If Theta is angle between the edges of the tank at gasoline level (at quarter tankness) and the center of the cylinder:

1/4 pi * R^2 = Theta/2 * R^2 - R^2 sin(Theta/2)cos(Theta/2)

Theta/2 - sin(Theta/2)cos(Theta/2) = 1/4 pi

The number of inches X for a quarter tank is then

X = R (1 - cos(Theta/2)) where R is 10 inches

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