Solve the problem. Round your answer to the nearest hundredth, if appropriate. $1)$ Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of $4\mathrm{.}00$ inches at the top and a height of $7\mathrm{.}00$ inches. At the instant when the water in the container is $6\mathrm{.}00$ inches deep, the surface level is falling at a rate of $1\mathrm{.}8\backslash (\backslash$mathrm$\{$in$\}./\backslash$mathrm$\{$sec$\}\backslash ).$ Find the rate at which water is being drained from the container. $2)$ Electrical systems are governed by Ohm's law, which states that $\backslash ($ V$=$I R $\backslash ),$ where $\backslash (\backslash$mathrm$\{$V$\}=\backslash )$ voltage, $\backslash (\backslash$mathrm$\{$I$\}=\backslash )$ current, and $\backslash (\backslash$mathrm$\{$R$\}=\backslash )$ resistance. If the current in an electrical system is decreasing at a rate of $\backslash (3\backslash$mathrm$\{$~A$\}/\backslash$mathrm$\{$s$\}\backslash )$ while the voltage remains constant at $14$ V $,$ at what rate is the resistance increasing $($in $\backslash (\backslash$Omega $/\backslash$mathrm$\{$sec$\}\backslash ))$ when the current is $48$ A $?($Do not round your answer.$)3)$ A man $6$ ft tall walks at a rate of $\backslash (2\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$sec$\}\backslash )$ away from a lamppost that is $12$ ft high. At what rate is the length of his shadow changing when he is $70$ ft away from the lamppost? $($Do not round your answer$)4)$ As the zoom lens in a camera moves in and out, the size of the rectangular image changes. Assume that the current image is $\backslash (4\backslash$mathrm$\{$~cm$\}\backslash$times $3\backslash$mathrm$\{$~cm$\}\backslash ).$ Find the rate at which the area of the image is changing $\backslash ((\backslash$mathrm$\{$dA$\}/\backslash$mathrm$\{$dt$\})\backslash )$ if the length of the image is changing at $\backslash (0\mathrm{.}6\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$s$\}\backslash )$ and the width of the image is changing at $\backslash (0\mathrm{.}2\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Your work should include:

$-$ a diagram

$-$ all variables clearly labeled including derivatives

$-$ the equation relating the variables in the problem

$-$ the work showing how you solved it and a statement of your solution including units of measure