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Question 2 (25 marks) Modelling our 5 x 5 x 5 Rubik's cube The following pictures show a curious Rubik's-cube-like structure that greets visitors to the Melbourne Museum. West The picture on the right shows what you see when you look at the cube from above using Google Earth Google Earth allows you to view many prominent buildings in 3D. Imagine that you are the maths wiz at Google whose job it is to create a 3D image of our cube for Google Earth. This means that you have to find coordinates of the corners of the square A, B, C, D visible from the top, as well as the coordinates of the points A', B', C', D' at which four edges of the cube intersect the ground. As indicated in the picture on the left, A is supposed to be connected to A' by such an edge, and similarly for B and B', C and O", and D and D'. It is your first day on the job and you are supposed to base your work on that of your predecessor, who got fired yesterday. Their notes are a terrible mess, but it is clear that they started modelling the cube by letting the (flat) ground coincide with the ry-plane and having the r-axis point North and the y-axis point West. Their notes don't tell you where the origin of the coordinate system is supposed to be, but wherever it may be, in this coordinate system we have B = (2.7997, 22.3302, 11.9406), B' = (1.9651, 19.8699, 0), D = (29.2866, 13.3456, 11.9406). 2 Your job is to determine the coordinates of the remaining corners of the building; the side length of the cube; the lengths of the four segments AA', BB', CC", DD'; the area of the quadrilateral A'B'C" D'; and, finally, the volume of the part of the cube that sits above the ground. Please start by summarising your results in the following way, and then provide explanations of how these results were derived afterwards. A = (*, *, *) [AA'| = *m B = (2.7997, 22.3302, 11.9406) [BB'| = * m C = (*, *, #) [CC'| = * m D = (29.2866, 13.3456, 11.9406) [DD'| = * m A' = (*, *, *) side length of cube = * m B' = (1.9651, 19.8699, 0) area of A'B'C'D' = * m- C' = (*, *, #) volume = * m D' = (*, *, * ) For any single one of these vectors/values that you get wrong, 1 markl will be deducted. One mistake that implies other mistakes will result in every single one of these mistakes being penalised in this way - Google Earth only accepts results that work! Please make absolutely sure that you double-check your results before you submit your report