What is the density of the metal sheet? In g/cm3

Question

A sheet of metal has an area of 1.32 ft2 and a height of 0.083 cm. The sheet weighs 255.2 g.

Answer 1

Hello, Madi,

We want an answerr with units of g/cm^3. This means we need to convert the area from ft^2 to cm^2 befiore we find the total volume by multiplying the area by the thinkness (height).

We can find:

1 meter = 3.28084 feet

100cm = 1 meter

Now convert the 1.32ft^2 into m^2:

(1.32ft^2)*(1 meter/3.28084 ft)^2 =

(1.32ft^2)*(1 meter^2/10.764 ft^2) = 0.1226 m^2

Note that we've squared the feet to meter conversion factor, and how the ft^2 now cancels out, leaving just m^2

Convert m^2 to cm^2:

(0.1226 m^2)*(100cm/1 meter)^2 =

(0.1226 m^2)*(10000cm^2/1 m^2) = 1226.32 cm^2

That is the area, so multiply by the height to obtain the volume of the metal sheet, in cm^3.

Volume = 101.78 cm^3

Now dividie the total mass of the sheet by this volume:

(255.2 grams/101.78 cm^3) = 2.507 g/cm^3

Change that to 2.51 g/cm^3 for 3 sig figs

Bob