How long of a line do you think you can draw with an avg. ball point pen using all its ink?

Answer 1

This would be a good example of a situation where we can use a Fermi approximation, which is a guess based on orders of magnitude. Let's start with asking how much ink is in an average pen. I think that the typical ink chamber is about 10 cm (0.1 m) long and has a radius close to 1 mm (0.001 m). That means the volume woud be pi*r^2*h ~= 5*(.001)^2*.1 = 5 x 10^-7 m^3. Now, how big is the cross-section of a marked line? Well, off the cuff, I think it's .1 mm (0.0001 m) wide and only .01 mm (0.00001 m) tall. It's hard to say, but I can tell that the line is much narrow than 1 mm, and its height isn't even visible from the side. So the cross-section has an area of 0.0001*0.00001 = 1 x 10^-9 m^2. The length of the line, then, would be the volume of ink divided by the cross-sectional area of the marked line, or (5 x 10^-7) / (1 x 10^-9) = 500 m, or half a kilometer.