Proposed Answer
Much more than 1 liter.
Make a guess.
Suppose the bathroom sink is about 15 inches across. That's actually not very big for a bathroom sink. But it makes up for the other estimate I'm going to make.
Suppose the sink is 7 1/2 inches deep at it's deepest point. So what you have is a 1/2 sphere. Figure this out in ccs. That way you have a simple conversion to make.
Conversion
1 in = 2.54 cm
7 1/2 in = x Cross multiply
x * 1 inch= 7 1/2 * 2.54
x = 6.5 * 2.54
x = 19.05 cm
x is actually the radius of the 1/2 sphere.
pi = 3.14
r = x = 19.05 cm
V = (4/3) pi * 19.05^3 / 2
V = 86831 / 6
V = 14471 ccs
1 L = 1000 cc
x = 14471 cc
x = 14.471 Liters. That's 14.5 times bigger than 1 Liter. Most sinks are about 7 1/2 inches deep but they are more across than 15 inches. So my answer is much more than 1 Liter. <<<<< Answer
Answer much more than a liter.