Q: A cylindrical can has a volume of 400πcm^3. The material for the top and bottom costs 2 cents per square centimeter. The material for the vertical surface costs 1 cent per square centimeter. Express the cost C of the materials used to make the can as a function of the radius r.

i know that a cylinder consists of 2 circles and the middle section, but would you call the middle section a rectangle...? or??? so far i got up to: cost= 2(0.02πr^2) + ?????????

could you take me step by step as I am really confuseddd???

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• Anonymous
9 years ago

• Anonymous
9 years ago

400π is the volume

volume for cylinder = π r² h

400π = π r² h

h = 400 / r²

area for the side surfaces = 2 π r h

= 2 π r (400 / r²)

= (800 π) / r

So the cost for the side surface (not include the top and bottom cost that you have calculated)

= \$ (0.01) x [ (800 π) / r ]

= (8 π) / r

• volume =V=pir^2h

400 =pi r^2 h

h=400/ pi r^2

surface area = 2 pir^2 +2pirh

cost =c(r)

=.01(2pir^2) +.02(2 pi 400/pir^2)

=.02pir^2 +16/r^2