Q4. The floor operator |x] on the real numbers is defined as follows: lx] = greatest integer lesser than x For example [3.6] = 3, 12.9999999] = 2, and [2] = 2. (a) (1) Write a function for the following piecewise continuous graph using the floor operator (don't forget to mention the domain). 25 3 (ii) You are to design an industrial bolt as shown below, where each cylinder has height 1 meter and radii 0.5, 1, 1.5, 2 and 2.5 meters respectively. Find the volume of the bolt. (ii) The bolt can be used to estimate volume of a cone with height 5 meters and circular base of radius 2.5 meters. Explain whether the volume you found in part (i) is an overestimation or an underestimation of the volume of cone described. (iv) Explain a strategy to find better estimates of volume of the cone using bolts of the kind described above. (v) Write a function y = f(x) such that it forms a cone with height 5 meters and a circular base of radius 2.5 meters when rotated around the x-axis (don't forget to mention the domain). (vi) Find the volume of a cone with height 5 meters and circular base of radius 2.5 meters using volumes of revolution approach. (b) Such a cone can also be described as the shape enclosed by the intersection of plane f(x,y) = 5 with the function g(x, y) = 2/x + y?. (1) 212 + y2. Sketch the shape enclosed by the plane f(x,y) = 5 and the function g(x, y) = (ii) Find the volume of the cone using a double integral formula. (C) Evaluate the integral below by changing it to cylindrical or spherical coordinates. 1V1-x JI (z + y) dzdydx 0.