Question

A cylindrical glass tube 10.8 cm in length is filled with mercury (density = 13.6 g/ml). (the volume of a cylinder of radius r and length h is v = πr2h.) the mass of mercury needed to fill the tube is 106.5 g. Calculate the inner diameter of the tube.

Answer 1

The volume,

$V = \frac{m}{\rho}$

Here, m is mass and $\rho$ is density.

Given, $m = 106.5 g$ and $\rho = 13.6 \ g/mL$.

Substituting these values in above equation, we get

$V = \frac{106.5 \ g}{13.6 \ g/mL}  = 7.8 \ mL$.

As the volume of cylinder,

$V= \pi r^2 h$

Given, $h =10.8 \ cm$

Therefore,

$7.8 \ mL = 3.14 \times r^2 \times 10.8 \ cm \\\\ r^2 = \frac{7.8}{3.14 \times 10.8} =   0.2 cm^2 \\\\ r =  0.5 cm$

We know, the inner diameter of cylindrical tube is the twice the radius,

$D = 2 r = 2 \times 0.5 cm = 1 \ cm$