Surface Area

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[Given]
Fiber Linear Density = 1 denier = 1 g/9000m
Fiber Density = 1.14 g/cm^3

[Find..]
Fiber surface area in cm^2/g
Assume that the fiber strand is a uniform cylinder

[Answer]
Surface area = 3,150 cm^2/g


....... how do i get to the answer? my professor gives us these notes:

Pi*D*L

Pi*D is the diameter of the top of the cylinder when it is cut vertically in half. and L is the height.

((Pi*D^2)/(4)) * L = volume of the cylinder

((Pi*D^2)/(4)) * L * Density = weight

..please help!

  • Surface Area -

    If it is a cylinder of length L

    volume= PI r^2 *L
    Surface area= PI*2(r)L

    mass=masslineardensiy*L
    density= mass/volume=1.14g/cm^3

    fiberarea/g= fiberarea/mass=
    PI*2*r*L/massdensity*V=
    PI*2r*L/(1.14g/cm^2 * PI*r^2*L)
    2cm^2/(1.14g*r)= 2/1.14r g/cm^2

    Now, r
    linear density=1g/9000m
    = mass/L= volumedensity*volume/L
    1g/9000m=1.14g/cm^3*PIr^2/L
    r^2=1cm^3/(1.14*9000m*PI)
    =1/(1.14*900000*PI) cm^2
    t hen find the sqrt root of that.

    final answer= 2/(1.14r) and it will give you your answer.

  • Surface Area -

    how to do surface area

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