Question

Question #a5b2a

Answer 1

The foil is only `0.0145"mm"` thick! This is much less than `1/1000` of an inch!

Explanation:

You have to convert to a consistent set of units. We shall use grams for the mass unit and centimeters for the length unit.

The area of the foil is then

`(75"ft"^2)×(30.48"cm"/{1"ft"})^2=69680"cm"^2`

The mass isj

`(9.6"oz")×(28.35"g/oz")=272.2"g"`

Now the volume of the foil is the mass divided by the density, and the density is given to only three significant figures. So we render the volume accordingly:

`(272.2"g")/(2.70"g"/{"cm"^3})=101"cm"^3`

And then the thickness is the volume divided by the area:

`(101"cm"^3)/(69680"cm"^2)=0.00145"cm"=0.0145"mm"`

Answer 2

`1.45 xx 10^(-2)`mm

Explanation:

The critical calculation here is the volume, after all of the conversions. The conversions are more tedious and a potential source of errors than anything relevant to the real question. We want a final answer in metric units (mm), so it may be best to first put all of the data into metric units at the millimeter level.

`75 ft^2 xx 92903.04 = 6967728 mm^2`
http://www.endmemo.com/convert/area.php

`1 cm^3 = 1000 mm^3`
`2.70 g/(cm^3) xx (0.001 cm^3)/(mm^3) = 0.0027 g/(mm^3)`

`9.6 oz xx 28.35 = 272.16 g`
http://www.endmemo.com/convert/weight%20and%20mass.php
NOW we have:
Density: `0.0027g/(mm)^3`
Mass: `272.16 g`
Area: `6967728 mm^2`

The desired thickness calculation is:
`T = "Mass"/("Density" xx "Area")` = `272.16/(0.0027 xx 6967728)` = `1.45 xx 10^(-2)`