Question

1. a column of mercury is contained in a cylindrical tube. this tube has a diameter of 8.0 mm, and a height of 1.20 m. given the density of mercury at 13.6 g/cm³, and that the volume of the tube can be calculated by the relation v = πr²h, calculate the mass of the mercury in the tube.

Explanation:

Step1: Convert units

First, convert the diameter and height to cm. The diameter $d = 8.0\ mm=0.8\ cm$, so the radius $r=\frac{d}{2}=\frac{0.8}{2}=0.4\ cm$. The height $h = 1.20\ m = 120\ cm$.

Step2: Calculate the volume of the tube

Use the formula $V=\pi r^{2}h$. Substitute $r = 0.4\ cm$ and $h=120\ cm$ into it. $V=\pi\times(0.4)^{2}\times120=\pi\times0.16\times120 = 19.2\pi\ cm^{3}\approx19.2\times3.14 = 60.288\ cm^{3}$.

Step3: Calculate the mass of mercury

Use the formula $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. Rearranging for $m$ gives $m=
ho V$. Given $
ho = 13.6\ g/cm^{3}$ and $V\approx60.288\ cm^{3}$, then $m = 13.6\times60.288=819.9168\ g\approx820\ g$.

Answer:

$820\ g$