Question

Bio-mimetic gel was used in the study of genetics and ultimately banded by the Federation. A Ferengi transport ship is carrying a 5-centimeter [cm] radius cylindrical tank of bio-mimetic gel to sell on the black market. A hydrostatic pressure probe located at the bottom of the tank reads 60 millimeters of mercury [mm Hg]. If the specific gravity of the gel is 8.9, what is the mass of gel contained in the tank in units of kilograms [kg]

Answer 1

m = 6.4 kg

Step-by-step explanation:

Now, we use the following equation to find the mass of the gel:

`P = \rho gh`

where,

P = (60 mm of Hg)(133.3 Pa/1 mm of Hg) = 7999.2 Pa = 7.99 KPa

ρ = density of gel =
`(m)/(V) = (m)/(\pi r^2 h)`

m = mass of gel = ?

r = radius of cylindrical tank = 5 cm = 0.05 m

h = height of tank

Therefore,

`7999.2 Pa = ((m)/(\pi(0.05\ m)^2\ h))(9.81\ m/s^2)h\\\\((7999.2\ Pa)(\pi)(0.05\ m)^2)/(9.81\ m/s^2) = m\\`

m = 6.4 kg