# SOLUTION: Hi Everyone, stuck in again on a weekend doing my maths !, having problems with this one please can someone help A circular-cylindrical oil drum is required to have a given surf

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: Hi Everyone, stuck in again on a weekend doing my maths !, having problems with this one please can someone help A circular-cylindrical oil drum is required to have a given surf      Log On

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 Click here to see ALL problems on Quadratic Equations Question 376236: Hi Everyone, stuck in again on a weekend doing my maths !, having problems with this one please can someone help A circular-cylindrical oil drum is required to have a given surface area S (including its lid and base), ie S is a constant. Find the proportions of the design which contain the greatest volume V . Thank You JohnAnswer by ankor@dixie-net.com(15660)   (Show Source): You can put this solution on YOUR website!A circular-cylindrical oil drum is required to have a given surface area S (including its lid and base), ie S is a constant. Find the proportions of the design which contain the greatest volume V . : Surface area: S = 2(pi*r^2) + (2*pi*h) : Volume: V = pi*r^2*h : Find the relationship between the surface area and the volume : = = Cancel pi*r = Therefore S = 2*(h+r) Assume a value: S = 120 2h + 2r = 120 h + r = 60 h = (60-r) : V = pi*r^2*(60-r): replace h with (60-r) Find Max volume. graph the equation y = 3.14*x^2*(60-x) Max volume occurs when r = 40 then h = 60 - 40 h = 20 : The proportion: = , we can say max volume when radius:height = 2:1