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# differentiation maths a level help watch

1. 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
2. Optimisation-the worst part of C2
3. Use a volune equation for a cylinder, then volume equals 2 liters so youll have an expression with r abd h
4. (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 so rearrange for .

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

iii.) for minimum surface area.
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
6. (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.
7. (Original post by RDKGames)
i.) Write out the volume of a cylinder. You know so rearrange for .

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

iii.) for minimum surface area.
Ok thankyou, I understand how to do it now, I'm still unsure of part iii) though
8. (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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Updated: January 28, 2017
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