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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.

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# Mass problem dealing with areas and lengths

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