Pascal demonstrated his principle by causing a wooden barrel full of water to burst when a small amount of additional water was poured into a long, thin tube extending vertically upward from the top of the barrel. Explain why this worked and estimate the magnitude of the force that burst the barrel's top (diameter \(0.42 \mathrm{~m}\) ) and the length of the tube (diameter \(6.0 \times 10^{-3} \mathrm{~m}\) ) if \(3.39 \times 10^{-4} \mathrm{~m}^{3}\) of water (less than 12 fluid ounces) was added.