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Thread: 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. $\displaystyle \frac{V(6)-V(3)}{6-3}$

    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. $\displaystyle V'(6)$

    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. $\displaystyle \frac{V(6)-V(3)}{6-3}$

    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. $\displaystyle V'(6)$

    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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