2a . Maximize the Volume of a Cone Place a line segment of fixed length L units in the first quadrant of the xy-plane with one endpoint at the origin, at an angle of 0 measured from the x-axis. Revolve this line segment about the y-axis to create a cone-shaped cup. 1. Sketch a picture of this line segment in the plane. Sketch a picture of a cup where 0 is large and sketch a picture of a cup when 0 is small. 2. Use the techniques associated with solids of revolution to compute the volume of such a cone. Your limits of integration should depend on the variable 0. 3. Find 0 that maximizes the volume of this cone, then find that volume. 4. What is the height of the water level when the glass (with 0 from #3) is half-full? 2b. Drinking Drinks You order a fancy cocktail (or mocktail) in a conical glass with the dimensions you found above (with L = 6 inches). It comes with a straw that extends 6 inches above the rim of the glass when leaning against the side of the glass. . When the glass is full, calculate the work it takes to drink all of the drink. . When the glass is half full, calculate the work it takes to drink all of the drink