Results 1 to 2 of 2

Thread: Linear approximation

  1. #1
    Member
    Joined
    Nov 2005
    Posts
    172

    Linear approximation

    I need help with this problem, i dont know how to set it up.

    Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.02000 cm thick to a hemispherical dome with a diameter of 45.00 meters.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by viet View Post
    I need help with this problem, i dont know how to set it up.

    Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.02000 cm thick to a hemispherical dome with a diameter of 45.00 meters.
    We have that volume of the hemisphere is a function of the radius, that is,
    $\displaystyle V(r)=\frac{2}{3}\pi r^3$
    Since $\displaystyle .02$ is a small number we have that the change in the derivative is approximately the change in the actual function, that is,
    $\displaystyle dV\approx \Delta V$
    Since,
    $\displaystyle \frac{dV}{dr}=2\pi r^2$
    The change in derivative is,
    $\displaystyle dV=2\pi r^2 dr$
    Where $\displaystyle dr=\Delta r$ the change in the radius.
    Which is, $\displaystyle +.02$
    Thus,
    $\displaystyle dV=2\pi (45)^2 (.02)$
    Thus,
    $\displaystyle dV=2\pi (2025)(.02)$
    Thus,
    $\displaystyle dV=81 \pi$
    That means the change in volume is approximately increased by $\displaystyle 81 \pi\mbox{ cm}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Approximation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 2nd 2010, 09:56 PM
  2. Linear Approximation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 11th 2009, 05:40 PM
  3. linear approximation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Sep 23rd 2008, 10:23 PM
  4. linear approximation y=
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Sep 10th 2008, 05:01 PM
  5. Linear Approximation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Nov 12th 2007, 07:11 PM

Search Tags


/mathhelpforum @mathhelpforum