Drink in a cylindrical can with height h and radius r, A) If the volume of the can is 87.5pi, state h in terms of r? B) Obtain the total surface area of the can in terms of r? C) Calculate the radius of the cylinder if the total surface area is minimum?

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Answer 1 · 2018-07-19T15:38:29

$r=3.52$

$V=pir^2h$

$87.5pi=pir^2h$

$(87.5pi)/(pir^2)=h$

$87.5/r^2=h$

$2pir^2+2pirh=SA$

Substitute for $h$ :

$2pir^2+2pir(87.5/r^2)=SA$

$2pir^2+(175pi)/r= SA$

graph{2pix^2+(175pi)/x [-45.7, 64.47, 222.62, 277.7]}

Graph the equation and look for when y is minimum but x still has to be positive