how do i find the area of a solid when i only have the density and the mass?

Question

this is the full question: Accomplished silver workers in india can pound silver into incredibly thin sheets, as thin as 3.00x10^-7 m. Find the area of such a sheet that can be formed from 1.00 kg of silver.

So the density is 3.00x10^-7, and the mass is 1.00 kg right? how do i get the area??

Answer 1

Density is mass / volume, so solve for volume first:

V = mass / density
V = 1 kg / density of silver

Pure silver has a density of 10.5 g/cm^3.

Dividing by 1000 g/kg:
Or 0.0105 kg / cm^3.

Multiplying by 1,000,000 cm^3 per m^3:
10,500 kg / m^3.

So silver is 10,500 kg per cubic meter.

The volume of 1 kg would be 1/10,500 m^3 = 9.52380952 × 10-5 m^3

Now volume is area times thickness.
V = A * thickness
A = V / thickness
A = 9.52380952 × 10-5 / 3 x 10^-7
A = 9.52380952 × 10-5 * 3 x 10^7
A = 2.85714286 × 10^3

So the answer is about 2.9 x 10^3 m² (2,857 sq. meters)

Answer 2

No 3.00E-7 is not the density. That is the thickness of the sheet. You will need to look up density of silver, however.

rho (silver) = .0105 kg/cm^3 = 10,500 kg/m^3

so, the area is simply...

A = (mass/thickness)/rho = 317.46 m^2

Answer 3

Divide mass by the density.