1. The first thing you have done is the simplest case, consider the following function defined a pieces () = { , 0 3 ; 3, 3 < < 6 } a) Draw the graph of this function. b) Obtain, using some software, the graph of the solid of revolution generated by (). c) Calculate the volume of this solid of revolution. d) Calculate the area of the generated surface. 2. Make a change to the previous number. Consider the following: () = { + , 0 ; , < < 20 } a) Determine values of the parameters so that the previous function is continuous and draw the graph of this function. b) Obtain, in some software, the graph of the solid of revolution generated by (). c) Calculate the volume of this solid of revolution. d) Calculate the area of the generated surface. e) Make the necessary modifications to obtain a volume of 10003 3. Finally, you are able to carry out your own custom design. Consider the following type of piecewise defined function. () = { () 0 () < < () Where () () must be transformations of some of the following functions, () is of free choice: sin() + cos() , ^/^, + ( ), 2/ ( + 1)+ / (1 ^2),5^4 + 3 / ^5+ 2 to. The function () must be continuous. b. The volume must be 10,000 cm3 c. Calculate the area. d. Can you smooth out your design? Have a discussion on this point.