Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    9
    ReputationRep:
    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
    • Community Assistant
    Offline

    11
    ReputationRep:
    Community Assistant
    Optimisation-the worst part of C2
    • Community Assistant
    Offline

    11
    ReputationRep:
    Community Assistant
    Use a volune equation for a cylinder, then volume equals 2 liters so youll have an expression with r abd h
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (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=2 so rearrange for h.

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

    iii.) \frac{dS}{dr}=0 for minimum surface area.
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (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
    Offline

    13
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by RDKGames)
    i.) Write out the volume of a cylinder. You know V=2 so rearrange for h.

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

    iii.) \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
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (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.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 28, 2017
Poll
Are you going to a festival?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.