(Solved): Question 1 (6 marks) A cylinder needs to be constructed using a recycled sphere as shown in Figure ...

Question 1 (6 marks) A cylinder needs to be constructed using a recycled sphere as shown in Figure Q1. Calculate the dimensions of the resulting cylinder and determine its maximum achievable volume. Provide a detailed explanation of the process and formulae used in your calculations.\r\nAs a contractor you are tasked in designing a floorplan for a new construction site. The site itself has a triangular shape, with one vertex forming an angle of \\( \\theta \\) degrees. The two sides connected to this vertex have lengths \\( \\mathrm{x} \\) and \\( \\mathrm{y} \\). To determine the area of this unique construction site, you can apply the following formula: \\[ \\operatorname{Area}(A)=\\frac{1}{2} x y \\sin \\theta \\] Consider your construction site is the following measurements: \\[ \\begin{array}{l} x=45.00 \\pm 0.05 \\text { meter } \\\\ y=35.00 \\pm 0.05 \\text { meter } \\end{array} \\] \\[ \\theta=\\pi / 6 \\pm 0.01 \\text { radians } \\] Calculate the maximum possible percentage error in the area calculation considering the given measurement uncertainties.