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 = (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 = (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 * r^2 * 10.8 \ cm \\\\ r^2 = (7.8)/(3.14 * 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 * 0.5 cm = 1 \ cm`