Cadbury is preparing a special edition of its famous egg-fondant. The new design of the chocolate...

Cadbury is preparing a special edition of its famous egg-fondant. The new design of the chocolate shell of the small egg is created from the following two paraboloids: z = 2−2x²−2y² and z = x² + y²−1. The x, y and z coordinates are given in centimeters. Answer the following questions using triple integrals and show steps.

a) Determine the volume of the egg using the rectangular coordinates

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 point to the Oz axis, determine the mass of the egg using the cylindrical coordinates. (We neglect here the mass of the chocolate shell.)

c) You share this egg with your teacher by cutting it with the horizontal plane z = c. Determine the value of the constant c to separate your egg into two pieces of equal volumes.Use rectangular coordinates

d) Determine the mass of each of the two pieces found in (c) using the cylindrical coordinates. Which piece should you keep to have the one with the most fondant?

*** fondant is the chocolate white milk inside the egg ****

Expert Solution

Colby Messinger answered 1 year ago

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