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Math Help - Estimating error using differentials

  1. #1
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    Estimating error using differentials

    Use differential to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a hemispherical dome with diameter 50cm.


    S= 2 pi r^2

    ds= 4 pi r dr.

    r= 50/2= 25 cm

    dr= 0.05cm

    So ds= 4 pi 25*0.05= 5 pi cm^2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by camherokid View Post
    Use differential to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a hemispherical dome with diameter 50cm.


    S= 2 pi r^2

    ds= 4 pi r dr.

    r= 50/2= 25 cm

    dr= 0.05cm

    So ds= 4 pi 25*0.05= 5 pi cm^2
    i may be wrong, but isn't the amount of paint talking about volume?
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  3. #3
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    So the answer must be this :

    V= 2/3* pi r^3

    dV= 2 pi r^2 dr.

    r= 50/2= 25 cm

    dr= 0.05cm

    So dV= 2 pi 25^2*0.05= 62.5 pi cm^3
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by camherokid View Post
    So the answer must be this :

    V= 2/3* pi r^3

    dV= 2 pi r^2 dr.

    r= 50/2= 25 cm

    dr= 0.05cm

    So dV= 2 pi 25^2*0.05= 62.5 pi cm^3
    yup, that looks about right
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