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Math Help - rate of change

  1. #1
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    Post rate of change

    please help me here.

    here is the problem:
    Use the formula V = (1/3)pi r2(h) for the volume of a right circular cylinder to find
    a. the average rate at which the volume of a right circular cylinder changes with the radius r as r increases from 3 cm to 6 cm.
    b. the instantaneous rate at which the volume of the right circular cylinder changes with r when r = 6 cm.

    I tried to solve it at home and I arrived at the answers:

    a. 3(pi)(h)

    b. 4(pi)(h)

    Are my answers correct?

    thanks
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mamen View Post
    please help me here.

    here is the problem:
    Use the formula V = (1/3)pi r2(h) for the volume of a right circular cylinder to find
    a. the average rate at which the volume of a right circular cylinder changes with the radius r as r increases from 3 cm to 6 cm.
    b. the instantaneous rate at which the volume of the right circular cylinder changes with r when r = 6 cm.

    I tried to solve it at home and I arrived at the answers:

    a. 3(pi)(h)

    b. 4(pi)(h)

    Are my answers correct?

    thanks
    For 1. \frac{V(6)-V(3)}{6-3}

    If this is what you did, your answer is right. Unless you made a mistake...You can see that the Average rate of change is nothing more than the slope of the secant line between the two points.

    For 2. V'(6)

    If you did this...

    Keep in mind that Instantaneous implies derivative.
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  3. #3
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    Quote Originally Posted by VonNemo19 View Post
    For 1. \frac{V(6)-V(3)}{6-3}

    If this is what you did, your answer is right. Unless you made a mistake...You can see that the Average rate of change is nothing more than the slope of the secant line between the two points.

    For 2. V'(6)

    If you did this...

    Keep in mind that Instantaneous implies derivative.
    Here is my solution.
    dy/dx=( 1/3 π(〖6)〗^(2 ) h- 1/3 π(〖3)〗^2 h)/(6-3)

    dy/dx=( 1/3 π36h- 1/3 π9h)/2

    dy/dx=( 1/3 π36h- 1/3 π9h)/2
    dy/dx=(12πh-3πh)/3
    dy/dx=9πh/3
    =3πh
    Solution:
    dy/dx=2/3 πrh
    At r = 6:
    dy/dx=2/3 π6h
    =4πh

    so is my solution and answer correct?
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