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Mass problem dealing with areas and lengths

  1. Aug 28, 2003 #1
    Hello again,

    The problem states that:

    Gold has a mass of 19.32 g for each cubic centimeter of volume.

    a) If 1.000 oz of gold, with a mass of 27.63 g, is pressed into a leaf of 1.000 micrometers thickness, what is the area of the leaf?

    b) If the gold is drawn out into a cylindrical fiber of radius 2.500 micrometers, what is the length of the fiber?

    Well,

    From the first part of the problem I got this ratio:

    1 cubic centimeter of gold : 19.32 g of gold

    For part A:

    I did a proportion:
    1 cubic centimeter / 19.32 g = x / 27.63 g
    x = 1.43 cubic centimeters = 1.43 x 10^-2 cubic meters

    but that is where i got stuck. i think that the x that i found is the volume for the 1 oz of gold, but how do i get the length of the leaf so I can get the area? also, if the problem says that the leaf has a certain thickness, then is the area they are looking for a surface area?

    For part B:

    I first changed the 2.500 micrometers into meters and got: 2.500 x 10^-6 meters

    the volume of a cylinder is: V = pi * r^2 * h

    then from part A, V = 0.143 cubic meters

    0.143 = pi * ( 2.500 x 10^6 )^2 * h

    solving for h, i got: h = 7.283 x 10^8 meters

    I think I can only get the right answer if I have the volume from part A correct, so I am unsure if my answer is correct.
     
  2. jcsd
  3. Aug 28, 2003 #2

    Tom Mattson

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    Gold Member

    OK, good start.

    You don't need the length. If the leaf is of uniform thickness (T), then the volume (V) and area (A) are related by:

    V=AT

    You can solve for the area directly.

    Yes.

    I do not have a calculator handy, so I can't check your number, but I can say that your method is correct. Assuming you did the calculator work correctly, this is A-OK.
     
  4. Sep 2, 2003 #3
    about converting the volume of 1.430 cm^3 into m^3, am i correct in doing the following:

    (1.430 cm^3)(1m/10^2cm)^3 = 1.430 x10^-6 m^3

    is that correct? or should i have just done this:

    (1.430 cm^3)(1m/10^2cm) = 1.430 x10^-2 m^3
     
  5. Sep 3, 2003 #4

    HallsofIvy

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    Your first calculation is correct. There are 100 cm in a m and so 100^3= 1000000 cubic cm in a cubic m. Although I wonder why yo are converting to cubic meters. Wouldn't it be easier to convert everything to cm?
     
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