Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    11
    ReputationRep:
    Water is pumped into a conical tank at a rate of 0.3m3s-1. The tank has the dimensions shown in the diagram, and the depth of the water is h metres at time t seconds. find an expression for dh/dt

    the cone has diameter 4m, and height 8m overall. (sorry for lack of diagram, q is from textbook)

    I keep getting 0.9/pi r^2 for my expression but apparently this is wrong...

    Can someone please help me on how to get the answer?
    Online

    18
    ReputationRep:
    (Original post by penelopecrux)
    Water is pumped into a conical tank at a rate of 0.3m3s-1. The tank has the dimensions shown in the diagram, and the depth of the water is h metres at time t seconds. find an expression for dh/dt

    the cone has diameter 4m, and height 8m overall. (sorry for lack of diagram, q is from textbook)

    I keep getting 0.9/pi r^2 for my expression but apparently this is wrong...

    Can someone please help me on how to get the answer?
    Whats the equation? Where the rest of the information? No one is responding because of this.
    Offline

    8
    ReputationRep:
    (Original post by penelopecrux)
    Water is pumped into a conical tank at a rate of 0.3m3s-1. The tank has the dimensions shown in the diagram, and the depth of the water is h metres at time t seconds. find an expression for dh/dt

    the cone has diameter 4m, and height 8m overall. (sorry for lack of diagram, q is from textbook)

    I keep getting 0.9/pi r^2 for my expression but apparently this is wrong...

    Can someone please help me on how to get the answer?
    The key element here is to get the relationship between the volume,V and the height, h of the water. From the cone dimensions you can see that the radius is 1/4 of the height. Now use the formula for the volume of a cone to create an equation connecting V and h. You should end up with V = (pi*h^3)/48. Now differentiate this to calculate dV/dh. Then use the chain rule and the fact that you are given dV/dt to calculate dh/dt. Hope that helps.
    • Thread Starter
    Offline

    11
    ReputationRep:
    (Original post by towcestermaths)
    the key element here is to get the relationship between the volume,v and the height, h of the water. From the cone dimensions you can see that the radius is 1/4 of the height. Now use the formula for the volume of a cone to create an equation connecting v and h. You should end up with v = (pi*h^3)/48. Now differentiate this to calculate dv/dh. Then use the chain rule and the fact that you are given dv/dt to calculate dh/dt. Hope that helps.
    thank you!!!!!!! Finally, someone with a brain!!!!!!!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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