Step 1. Convert the area of the foil to square centimetres.
#"A" = 75 color(red)(cancel(color(black)("ft")))^2 × ((12 color(red)(cancel(color(black)("in"))))/(1 color(red)(cancel(color(black)("ft")))))^2 × (("2.54 cm")/(1 color(red)(cancel(color(black)("in")))))^2 = 6.97 × 10^4color(white)(l) "cm"^2#
Step 2. Convert the mass of the foil to grams.
#"Mass" = 9.6 color(red)(cancel(color(black)("oz"))) × (1 color(red)(cancel(color(black)("lb"))))/(16 color(red)(cancel(color(black)( "oz")))) × "454 g"/(1 color(red)(cancel(color(black)("lb")))) = "272 g"#
Step 3. Calculate the volume of the foil.
The formula for the density of an object is
#color(blue)(bar(ul(|color(white)(a/a) ρ = m/V color(white)(a/a)|)))" "#
where
#ρ# = density of the object
#m# = mass of the object
#V# = volume of the object
We can rearrange the formula to get
#V = m/ρ#
∴ #V = 272 color(red)(cancel(color(black)("g"))) × ("1 cm"^3)/(2.70 color(red)(cancel(color(black)("g")))) = "101 cm"^3#
Step 4. Calculate the thickness of the foil.
The formula for the volume of a rectangular solid is
#color(blue)(bar(ul(|color(white)(a/a) V = Ah color(white)(a/a)|)))" "#
where
#V# = volume of the solid
#A# = area of the solid
#h# = height (or thickness) of the solid.
We can rearrange this formula to
#h = V/A#
∴ #h = (101 stackrelcolor(blue)("cm")(color(red)(cancel(color(black)("cm"^3)))))/(6.97 × 10^4 color(red)(cancel(color(black)("cm"^2)))) = 1.45 × 10^"-3"color(white)(l) "cm"#
Step 5. Convert the thickness to millimetres.
#1.45 × 10^"-3" color(red)(cancel(color(black)("cm"))) × "10 mm"/(1 color(red)(cancel(color(black)("cm")))) = "0.014 mm"#
