help Part B (Square Cake Tins):Let I (cm) be the side length of the square tinplate and let x (cm) be the side length of the square cuts to bemade.(a)V(x) = 4x3 – 40x² + 100x cm³.Hence, determine V'(x) and find the exact value of x which will maximise the volume of the cake tin.Given l = 10cm, show that the volume of the cake tin can be expressed as(b)Further this investigation by determining the exact value of x for at least two other values of l cm(side length of square tinplate).Present a conjecture based on a square piece of tinplate of side length l cm, which when a square is(c)cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will beobtained. Show sufficient working to support your conjecture. Part A (Preliminary):Consider a 30cm square of tinplate.(a)Determine the volume of the cake tin if a 4cm square is cut from each corner and the sides folded toform the tin.(b)Determine the volume of the cake tin if the following squares are cut from each corner of the tinplate:(i)2cm(ii)5cm(ii)8cm(c)be expressed as V(x) = 4x3 – 120x2 + 900x cm', where x (cm) is the size of the square cut fromeach corner.Given the length of each side of the square tinplate is 30cm, show that the volume of the cake tin can(d)Show, using graphical and/or calculus methods, that the optimal volume is when a 5cm square iscut from each corner.30cm

Since you have posted more than one question with multiple sub-parts, we solve only the first…

Part A (Preliminary): Consider a 30cm square of tinplate. (a) Determine the volume of the cake tin if a 4cm square is cut from each corner and the sides folded to form the tin. (b) Determine the volume of the cake tin if the following squares are cut from each corner of the tinplate: (i) 2cm (ii) 5cm (ii) 8cm (c) Given the length of each side of the square tinplate is 30cm, show that the volume of the cake tin car be expressed as V(x) = 4x3 – 120x2 + 900x cm³, where x (cm) is the size of the square cut from each corner. 30 cm