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1) Cell Walls. Although these quantities vary from one type of cell to another, a cell can be 2.00 μm in diameter with a cell wall that is 50.0 nm thick. If the density (mass divided by volume) of the wall material is the same as that of pure water (1000 kg/m2), what is the mass (in ng) of the cell wall, assuming the cell to be spherical and the wall to be a very thin spherical shell? Gas Mileage. A US gallon is 231 cubic inches. An Imperial gallon, often used in England and other British Commonwealth countries, is 277.42 cubic inches. Note that 1 inch 2) 2.54 cm (exactly). a. Say that on a particular day. gasoline in Great Falls, Montana is selling for 3.50 USD per US gallon. At the same time, gasoline in Lethbridge, Alberta is 5.00 CAD per Imperial gallon. If 1.00 CAD - 0.75 USD, on which side of the border is gas cheaper? Start by converting both prices to CAD per litre( L- 1000 cubic centimetres). Remember to show all of your work! (8) If you are driving down to Great Falls (perhaps to buy gas?) at 110 km/h, how fast are you going in miles per hour (mph) and metres per second? (2) b.

Answer 1

1)

Volume of spherical shell wall ( cell wall ) is $V=\frac{4}{3}\pi (R^3-r^3)$

Where $R$ is outer radius of spherical shell, $r$ is inner radius of spherical shell.

Diameter of cell $d=2\,\mu m=2*10^{-6}\,m$

Radius of cell $d/2=1\,\mu m=1*10^{-6}\,m$

Outer radius of cell is $R=d/2=1*10^{-6}\,m$

Inner radius of cell is $r=R-50\,nm=1*10^{-6}-50*10^{-9}=0.95*10^{-6}\,m$

Density of cell wall $\rho=1000\,kg/m^3$

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

Mass of cell wall is $M=\rho V=1000*\frac{4}{3}\pi\left [ (1*10^{-6})^3-(0.95*10^{-6})^3 \right ]$

$M=5.97*10^{-16}\,kg=5.97*10^{-13}\,g=5.97*10^{-4}\,ng$