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Math Help - Percentage Error

  1. #1
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    Percentage Error

    Hi guys,

    I'm stuck on a word problem and could use a little help. I did the work, just not real confident in it.

    Company manufactures spherical ball bearing with radius 1 cm and percentage error in radius must be no more than 1%.

    a) Find approximate percentage error for surface area of ball bearing?
    b) Find range of radii possible.
    c) What range of surface area possible.
    ---> Ok, so what we're given is r = 1 cm and dr = +/- .01 cm (correct?)

    a) Percentage error surface area
    ---> S=4(pi)r^2
    --->dS=8(pi)r(dr) = 8(pi)(1cm)(+/- .01 cm) = +/- .25133 cm^2
    ---> Percent error = dS/S
    -----------> S=4(pi)(1cm)^2= 12.56637 cm^2
    ----------->dS/S = (+/- .25133 cm^2)/(12.56637 cm^2) = .020000 = 2%
    (Correct?)

    b) Range of radii
    -->would be: 1 cm + .01 cm = 1.01 and 1 cm - .01 = .99 cm
    -->RANGE = .99 - 1.01 or +/ .01 cm (correct?...just seems a little simple)

    c) Range Surface area
    --> S = 4(pi)r^2
    --> dS = 8(pi)r(dr) = 8(pi)(1cm)(+/- .01 cm) = +/- .25133 cm^2
    (correct?)

    EDIT: Perhaps on C, the range would be (12.56637 + .25133 = 12.8177 cm^2 and 12.56637 - .25133 = 12.31504 cm^2

    Thanks for the help. Will return the favor if you'd post a link to your problem.
    Last edited by Mathless; April 5th 2010 at 03:07 PM.
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722
    Quote Originally Posted by Mathless View Post
    Hi guys,

    I'm stuck on a word problem and could use a little help. I did the work, just not real confident in it.



    ---> Ok, so what we're given is r = 1 cm and dr = +/- .01 cm (correct?)

    a) Percentage error surface area
    ---> S=4(pi)r^2
    --->dS=8(pi)r(dr) = 8(pi)(1cm)(+/- .01 cm) = +/- .25133 cm^2
    ---> Percent error = dS/S
    -----------> S=4(pi)(1cm)^2= 12.56637 cm^2
    ----------->dS/S = (+/- .25133 cm^2)/(12.56637 cm^2) = .020000 = 2%
    (Correct?)

    b) Range of radii
    -->would be: 1 cm + .01 cm = 1.01 and 1 cm - .01 = .99 cm
    -->RANGE = .99 - 1.01 or +/ .01 cm (correct?...just seems a little simple)

    c) Range Surface area
    --> S = 4(pi)r^2
    --> dS = 8(pi)r(dr) = 8(pi)(1cm)(+/- .01 cm) = +/- .25133 cm^2
    (correct?)

    EDIT: Perhaps on C, the range would be (12.56637 + .25133 = 12.8177 cm^2 and 12.56637 - .25133 = 12.31504 cm^2

    Thanks for the help. Will return the favor if you'd post a link to your problem.
    I think your method for c) is wrong.

    Formula for surface area of sphere is,

    4 \pi r^2.

    Your range of radii is 0.99 - 1.01.

    So just substitute these two values into the formula for surface area to get...

    4 \pi 0.99^2 = 12.31629984

    4 \pi 1.01^2 = 12.81895467
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