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Math Help - Related Rate HELP

  1. #1
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    Related Rate HELP

    I have about 20 related rate problems that I just cannot get a grasp on. I'll post a couple, and anyone who can show me how to work them would be greatly appreciated. I think if I can see a couple worked out, I can get the rest of them alright.

    1. A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume is 128pi cubic inches. At what rate is the height changing when the radius is 1.8 inches?

    2. A sphirical balloon is inflated at a rate of 16 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 2 feet?

    Thanks for all the help; for some reason this stuff just doesn't click.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by claybird View Post
    I have about 20 related rate problems that I just cannot get a grasp on. I'll post a couple, and anyone who can show me how to work them would be greatly appreciated. I think if I can see a couple worked out, I can get the rest of them alright.

    2. A sphirical balloon is inflated at a rate of 16 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 2 feet?

    Thanks for all the help; for some reason this stuff just doesn't click.
    Recall that the volume of the sphere is defined as V=\tfrac{4}{3}\pi r^3.

    We are given \frac{\,dV}{\,dt}=16\frac{ft^3}{s}

    We want to find \frac{\,dr}{\,dt} when r=2~ft.

    Thus, we should differentiate the volume equation:

    V=\tfrac{4}{3}\pi r^3\implies \frac{\,dV}{\,dt}=4\pi r^2\frac{\,dr}{\,dt}

    We know \frac{\,dV}{\,dt} and r. Now it should be easy to find \frac{\,dr}{\,dt}

    --Chris
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