1. Background: A company manufactures solid objects known as gizmoids made of variable density plastic. In the company's design specifications, a gizmoid is modelled as a solid region V satisfying the conditions: x² + y² + ² ≤1 and z≥ √3(x² + y²). The mass per unit volume (mass density) of V is p(x, y, z) = 10z. The point of the gizmoid at (0,0,0) is referred to as the tip. The company also manufactures the much sought-after delure gizmoids. These are identical to regular gizmoids, except that the part of the gizmoid more than 0.9 units from the tip is made of gold rather than plastic. [Note that the set of all points in a gizmoid that are exactly 0.9 units. from the tip form part of the surface of a sphere of radius 0.9. This means that the part of a deluxe gizmoid made of gold has two spherical boundary surfaces.] (a) Sketch V. (b) Calculate the mass of a gizmoid, using cylindrical coordinates. (c) Calculate the mass of a gizmoid, using spherical coordinates. (d) Determine the exact volume of gold required to manufacture 1,000 deluxe gizmoids. (e) Assuming that gold has a constant density (mass per unit volume) of 19, use the MATLAB symbolic toolbox to calculate the mass of a deluxe gizmoid. [Hint: Use spherical coordinates.]