Cadbury is preparing a special edition of its famousegg-fondant. The new design of the chocolate shell of the small eggis created from the following two paraboloids: z =2?2x2?2y2 and z = x2 +y2?1. The x, y and z coordinates are given incentimeters. Answer the following questions using tripleintegrals and show steps.
a) Determine the volume of the egg using the rectangularcoordinates
b) Knowing that the density of the fondant inside the egg (in g/ cm3) at a point (x, y, z) is 3 times the distance from this pointto the Oz axis, determine the mass of the egg using thecylindrical coordinates. (We neglect here the mass of thechocolate shell.)
c) You share this egg with your teacher by cutting it with thehorizontal plane z = c. Determine the value of the constant c toseparate your egg into two pieces of equal volumes.Userectangular coordinates
d) Determine the mass of each of the two pieces found in (c)using the cylindrical coordinates. Which pieceshould you keep to have the one with the most fondant?
*** fondant is the chocolate white milk inside the egg ****
