2. A homeware company has been approached to manufacture a cake tin in th of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversar games launch. The base of the cake tin has a characteristic dimension y and illustrated in Figure 1 below, you should assume the top and bottom of the can be represented by semi-circles. The vertical sides of the cake tin have a h. As the company's resident mathematician, you need to find the values o that minimise the internal surface area of the cake tin given that the volum tin is Vfixed. 2r Figure 1 - Plan view of the "ghost" cake tin base. (a) Show that the Volume (V) of the cake tin as a function of r and h is V = 2(+1) r²h (b) Show that the Surface area (S) of the cake tin as a function of r and his S = 2 2(+1)² + 2(x+1)rh

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