(b) A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder with a hemispher

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B A Steel Storage Tank For Propane Gas Is To Be Constructed In The Shape Of A Right Circular Cylinder With A Hemispher 1 (50.32 KiB) Viewed 13 times

(b) A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder with a hemisphere at each end. Suppose the cylinder has length € metres and radius r metres. l (i) Write down an expression for the volume V of the storage tank (in terms of l and r). (ii) Write down an expression for the surface area A of the storage tank (in terms off and r). (iii) Using the result of part (ii), write V as a function of r and A. (That is, eliminate (.) (iv) A client has ordered a tank, but can only afford a tank with a surface area of A = 40 square metres. Given this constraint, write V = V(r). (v) The client requires the tank to have volume V = 10 cubic metres. Use Newton's method, with an initial guess of ro = 2 to find an approximation (accurate to three decimal places) to value of r which produces a volume of 10 cubic metres. (Newton's method for solving f(r) = 0: f(rn) Tn+1 = Tn for n=0,1,2,...) f'(rn) 20 marks)