Like Problem $11-42$

Statement

To reduce the drag coefficient and thus to improve the fuel efficiency of cars, the design of side rearview mirrors has changed drastically in recent decades from a simple circular plate to a streamlined shape. Determine the amount of fuel and money saved per year as a result of replacing a $\backslash (15\mathrm{.}0-\backslash$mathrm$\{$cm$\}\backslash )-$diameter flat mirror by one with a hemispherical back, as shown in the figure. Assume the car is driven $21000\mathrm{.}0$ km a year at an average speed of $\backslash (80\mathrm{.}0\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ).$ Take the density and price of gasoline to be $\backslash (0\mathrm{.}75\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$L$\}\backslash )$ and $\backslash (\backslash$$ $1\mathrm{.}1/\backslash$mathrm$\{$L$\}\backslash ),$ respectively; the heating value of gasoline to be $\backslash (44000\mathrm{.}0\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$; and the overall efficiency of the drive train to be $27\mathrm{.}0$ percent.