$(4$ points$)$ A $40$ meter chain hangs vertically from a cylinder attached to a winch. Assume there is now friction in the system and the chain has a density of $5k\frac{g}{m}.$ How much work is required to wind only the first $12$ meters of the chain around the winch if there is a $25$ kg block attached to the end of the chain?

$(4$ points$)$ A conical tank, shown below, is full of water. Draw a $y-$axis $($in the vertical direction$)$ next to the figure and label the $y-$values corresponding to the top and bottom of the tank. Set up the integral needed to find the total amount of work required to pump all of the water out of the top of the tank. Use $1000k\frac{g}{m^3}$ for the density of water and use $g$ for acceleration due to gravity. $($Hint: Use similar triangles to determine the radius of a cross$-$section of the water.$)$