I don't understand this question! help!?

Question

A 200.0 mg piece of gold can be hammered into a sheet that is 2.4 ft. by 10 ft.

a) What is the thickness of the sheet in m?

b) Quote the answer using the SI prefix so hat there is no exponent needed.

Thank you!

Answer 1

Its a volume and density question the volume  is

density = mass/volume

the density of gold is 19.3 g/cm3  http://en.wikipedia.org/wiki/Gold

convert mg to grams by dividing by 1000

volume=mass/density =  0.2g/19.3=0.01036 cm^3 of gold

v = length * width * height

convert the ft to cm

1 ft = 30.48 cm  http://www.worldwidemetric.com/metcal.ht...

2.4 ft * 30.48 = 73.152 cm

10ft * 30.48= 304.8 cm

from the density/mass equation above we know the total volume is 3.86 cm^3 of gold

use the formula v = length * width * height

0.01036 cm^3= 304.8 * 73.152 * height

height = 0.000000464 cm

there are 100 cm in a meter so we divide the answer by 100 to get 0.00000000464 cm m and this is the thickness. i think it is 4.64 x 10^-9 m

4.64 nano meters is correct

Answer 2

Gold density: 19.3 g/cm³

You have 200.0 mg, which is 2×10^-2 g. This means you have a volume of 2×10^-2/19.3 = 0.0103627 cm³ of gold.

The area of the sheet will be 73.152×304.8 cm² = 22296.7296 cm². Divide the volume by the area to get the thickness in cm, then convert to m by dividing by 100.

4.6476 × 10^-9 m thick.

This is the equivalent of 4.6476 nanometres (nm).