Gold, has a mass of 19.32g for wach cubic centimeter of volume, is most ductile metal and can be pressed into a thin leaf or drawn out into long fiber.
-If a sample of gold, with a mass of 27.63g is pressed into a leaf of 1.000micometers thickness, what is the area of the leaf?
-If instead the gold is drawn out into cylinder fiber of radius 2.500 micrometers, what is the length of the fiber?
my work:I think I've figured it out:
thickness is 1.000 micrometers
density=19.32
mass: 27.63
area=(27.63)/((19.32)(1.000))=1.43 (of leaf)
Volume=AxD=1.43x19.32=27.63
27.63=(pie)r^2L
27.63=(pie)(2.500)^2L=1.408 Length of leaf?
I don't follow all of your calculations although they may be correct. For the first part of the question, you don't tell us the shape of the leaf. We calculate the volume from the density.
mass = volume x density
27.63g = v x 19.32g/cc
v = 27.63/19.32 = 1.430 g/cc
That will be the volume of the leaf but without knowing if it is a circle, a rectangle, a square, or what, we can't calculate the area.
For the second part, the volume of a cylinder is volume = pi*r^2h (note pi is the Greek letter for pi and not the pie we eat).
Just plug in the values for v, pi, and r and calcualte the height (that is the length) in centimeters.
I hope this helps.
I think for the first one we could have V=A*h where A is the area and h is the height.
I'm not sure the shape is needed there.
still confused:(
Ok, here's what you've given us:
"Gold, has a mass of 19.32g for wach cubic centimeter of volume, is most ductile metal and can be pressed into a thin leaf or drawn out into long fiber.
-If a sample of gold, with a mass of 27.63g is pressed into a leaf of 1.000micometers thickness, what is the area of the leaf?
-If instead the gold is drawn out into cylinder fiber of radius 2.500 micrometers, what is the length of the fiber?"
We have mass = 19.32g (I think you meant for 'each' cm^3. Therefore we know the density. Let's summarize
density = 19.32g/cm^3
mass = 27.63g
density = mass/volume, or
volume = density/mass
(I'll let you do the calculations and show work here.)
The first question is:
"-If a sample of gold, with a mass of 27.63g is pressed into a leaf of 1.000micometers thickness, what is the area of the leaf? "
Therefore height (or thickness) = 1.000micometers
The units need to be compatible, so you want to convert this to cm's
We also know that V=A*h (you should know this or see how to derive it)
That is, the surface area times the height will give the volume -if the height is uniform. For this problem it is uniform.
Therefore, to calculate the area take A=V/h
I'm not sure that you converted the micrometers to cm's. If you do this, you should get an area in square cm's, i.e., Acm^2.
Does this help?
Yes that does help thank you. But what about the length? Is there a formula that will calculate the length for this?
The area is the question for the first part. The length is for the second part of the question and I detailed how to do that.
The fiber is cylinder
For the 2nd question, it appears to me that DrBob222 did suggest how to solve this problem, so I'll only attempt a clarification.
It seems we want to transform the mass of gold into a cylindrical piece of wire.
This problem is similar to the first, but this time we know (or should know) the area for a cross section of a cylinder is A = pi*r^2. Further, we know that the mass has to have the same volume, regardless of it's shape. Whether it's a cube, sphere or cylinder is immaterial. For the 2nd problem we need to convert the radius to cm's again. We then have
V = A*h = pi*r^2*h
I've used h for the height, but you could use l too; that's the dimension we want to find.
Use the volume you calculated earlier, determine the radius r in cm's and do the calculations. Show your work so we know where the difficulties are.
How do you solve this problem?
What is the volume of a fish tank that is 80 cm long, 32 cm wide and 26 cm high?
1 answer