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    these questions are giving me trouble, so there must be a fundamental problem with my understanding.

    ok, so the question is asking for dx/dt

    we know the cross sectional area is increasing, so we know dA/dt

    so, it would be logical to form an equation based on: dx/dt = (dx/dA)(dA/dt)

    we know the volume is (\pi r^2)(height)

    so, V=( \pi x^2)(5x), therefore V=( 5 \pi x^3)

    dV/dx = 15 \pi x^2

    dA/dx = 30 \pi x
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    (Original post by Maths&physics)
    dV/dt = 15 \pi x^2
    This is incorrect. You want to say here that dV/dx = 15 pi x^2 instead, then you have all you need for the chain rule.
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    (Original post by RDKGames)
    This is incorrect. You want to say here that dV/dx = 15 pi x^2 instead, then you have all you need for the chain rule.
    I meant: dV/dx = 15 \pi x^2

    I was copy and pasting to save time. however, my dA/dx = 30 \pi x doesn't give me the right answer.
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    (Original post by Maths&physics)
    I meant: dV/dx = 15 \pi x^2

    I was copy and pasting to save time. however, my dA/dx = 30 \pi x doesn't give me the right answer.
    OK I got lost in your working tbh.

    \dfrac{dx}{dt} = \dfrac{dx}{dA} \cdot \dfrac{dA}{dt} is correct. We know dA/dt from the context so we just need dx/dA.

    The cross sectional area is given by A=\pi x^2 since it's just a circle.
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    (Original post by RDKGames)
    OK I got lost in your working tbh.

    \dfrac{dx}{dt} = \dfrac{dx}{dA} \cdot \dfrac{dA}{dt} is correct. We know dA/dt from the context so we just need dx/dA.

    The cross sectional area is given by A=\pi x^2 since it's just a circle.
    what do you mean its just a circle? its a cylinder?
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    (Original post by Maths&physics)
    what do you mean its just a circle? its a cylinder?
    The cross-section of a cylinder is a circle. By A you are referring to the area of it.
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    (Original post by RDKGames)
    The cross-section of a cylinder is a circle. By A you are referring to the area of it.
    because the cross sectional area is increasing, we only use the cross sectional area in the equation?
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    (Original post by Maths&physics)
    because the cross sectional area is increasing, we only use the cross sectional area in the equation?
    Yes. We are not told nothing about the volume, so no need to work with it.
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    (Original post by RDKGames)
    Yes. We are not told anything about the volume, so no need to work with it.
    brilliant. thank you
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    (Original post by RDKGames)
    Yes. We are not told nothing about the volume, so no need to work with it.
    one last thing: what do they mean by: a "right" circular cylindrical metal rod.
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    (Original post by Maths&physics)
    one last thing: what do they mean by: a "right" circular cylindrical metal rod.
    The angle between the circle as a base and the curved surface is 90 degrees.

    A non-right circular cylinder would be something like this:

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    (Original post by RDKGames)
    The angle between the circle as a base and the curved surface is 90 degrees.

    A non-right circular cylinder would be something like this:


    ah ok, but they didn't write: right angled. but thanks.
 
 
 
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