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differentiation maths a level help

a cylindrical can with height h metres and radius r metres has a capacity of 2 litres i) find an expression for h in terms of r
ii) hence find an expression for the surface area of the can in terms of r only
iii) find the value of r which minimises the surface are of the can
Reply 1
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Rexar
11
Optimisation-the worst part of C2
Reply 2
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Rexar
11
Use a volune equation for a cylinder, then volume equals 2 liters so youll have an expression with r abd h
Original post by imaan2121
a cylindrical can with height h metres and radius r metres has a capacity of 2 litres i) find an expression for h in terms of r
ii) hence find an expression for the surface area of the can in terms of r only
iii) find the value of r which minimises the surface are of the can


i.) Write out the volume of a cylinder. You know V=2V=2 so rearrange for hh.

ii.) Write out the formula for the surface area of the cylinder - SS. Substitute for hh from part i.

iii.) dSdr=0\frac{dS}{dr}=0 for minimum surface area.
(edited 7 years ago)
Original post by Google22
i) V = 2
2 = Πr²h
h = 2/Πr²

ii) Surface Area = 2Πr² + 2Πrh = 2Πr² + 4r

iii) dA/dr = 4Πr + 40 = 4Πr + 40 = 4(Πr + 1)
Πr = -1
r = -1/ Π

Surface Area = 2Π(-1/Π) + 4(-1/Π) = -2 - (4/Π)


Not only do you attempt to post a full solution, but you also get it wrong... Double nope.

@Mr M
(edited 7 years ago)
Original post by RDKGames
Not only do you attempt to post a full solution, but you also get it wrong... Double nope.

@Mr M


Oh right, I'm new here.
Reply 6
Avatar for imaan2121
imaan2121
OP
9
Original post by RDKGames
i.) Write out the volume of a cylinder. You know V=2V=2 so rearrange for hh.

ii.) Write out the formula for the surface area of the cylinder - SS. Substitute for hh from part i.

iii.) dSdr=0\frac{dS}{dr}=0 for minimum surface area.


Ok thankyou, I understand how to do it now, I'm still unsure of part iii) though
Original post by imaan2121
Ok thankyou, I understand how to do it now, I'm still unsure of part iii) though


You have expressed the surface area in terms of r. You can differentiate it and set it equal to 0 and solve for r to see when it is a minimum.

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