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

    9
    ReputationRep:
    Leaking oil is forming a circular patch on the surface of the sea. The area of the patch is increasing at a rate of 250 square metres per hour. Find the rate at which the radius of the patch is increasing at the instant when the area of the patch is 1900 square metres. Give your answer correct to 2 significant figures.

    How do i approach this question?
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by elvss567)
    Leaking oil is forming a circular patch on the surface of the sea. The area of the patch is increasing at a rate of 250 square metres per hour. Find the rate at which the radius of the patch is increasing at the instant when the area of the patch is 1900 square metres. Give your answer correct to 2 significant figures.

    How do i approach this question?
    Translate the words into maths:

    The area of the patch is increasing at a rate of 250 square metres per hour

    So the rate of change of area is +250

    So \frac{dA}{dt} = 250

    Often the units give you a clue. Here square metres per hour suggests \frac{dA}{dt}

    Are you able to carry on from here?
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by Notnek)
    Translate the words into maths:

    The area of the patch is increasing at a rate of 250 square metres per hour

    So the rate of change of area is +250

    So \frac{dA}{dt} = 250

    Often the units give you a clue. Here square metres per hour suggests \frac{dA}{dt}

    Are you able to carry on from here?
    so i have to find dA/dt when area=1900.
    dA/dt = dA/dv * dV/dt
    = dA/dr * dr/dV * dV/dt
    is this right so far?
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by elvss567)
    so i have to find dA/dt when area=1900.
    dA/dt = dA/dv * dV/dt
    = dA/dr * dr/dV * dV/dt
    is this right so far?
    No you need to find the rate of increase of the radius so you need to find \frac{dr}{dt}. I'm not sure what your V is for?
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by Notnek)
    No you need to find the rate of increase of the radius so you need to find \frac{dr}{dt}. I'm not sure what your V is for?
    oh okay. i probably made a mistake. how do i calculate dr/dt? do i use the formula for area of the circle(pir^2) for it or something?
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by elvss567)
    oh okay. i probably made a mistake. how do i calculate dr/dt? do i use the formula for area of the circle(pir^2) for it or something?
    Yes that formula gives you A in terms of r and you can use this to find \frac{dA}{dr}. Then you can use the chain rule in a similar way to your previous attempt.
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by Notnek)
    Yes that formula gives you A in terms of r and you can use this to find \frac{dA}{dr}. Then you can use the chain rule in a similar way to your previous attempt.
    thankyou
 
 
 
  • 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.

  • Will you be richer or poorer than your parents?
    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.