Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    The volume of a cone is given by V = \frac{1}{3} \pi L^3 sin^2x cosx
    given that L is constant and x varies find the maximum value of v in terms of L and  \pi
    Online

    21
    ReputationRep:
    Isn't this just a C2 question with C3 differentiation? If you know how to differentiate V and solve V' = 0 then you'll get the answer in no time.
    • Very Important Poster
    Online

    21
    ReputationRep:
    Very Important Poster
    (Original post by shawn_o1)
    Isn't this just a C2 question with C3 differentiation? If you know how to differentiate V and solve V' = 0 then you'll get the answer in no time.
    Product rule is required (C3).

    What have you tried so far OP?
    • Thread Starter
    Offline

    14
    ReputationRep:
    does dy/dx=  (\pi l^2 sin^2x cosx) + (\frac{1}{3} \pi L^3 sinx ( 2cos^2x- Sin^2x))
    Offline

    1
    ReputationRep:
    (Original post by AlexS101)
    does dy/dx=  (\pi l^2 sin^2x cosx) + (\frac{1}{3} \pi L^3 sinx ( 2cos^2x- Sin^2x))

    it says that L is constant so you don't have to treat it as a variable. you have to use the product rule. you have cos(x)(sin(x))^2, so the differential is 2cos(x)sin(x)cos(x) -sin^3(x) =0

    when sin(x) = 0 then x =0 so that means there is no volume as it is the minimum solution.
    that leaves you with 2cos^2(x)-sin^2(x)=0
    re-arange to either get
    cos(x)=1/sqrt(3)
    or
    tan(x) = sqrt(2)
    or
    sin(x) = sqrt(2/3)
    subbing this back into the formula for V, V(max) = (pi/3)(L^3)(2/3sqrt(3))
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 21, 2015
Poll
Do you think parents should charge rent?
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.