Question #a5b2a

2 Answers
Dec 25, 2017

Answer:

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"#

Dec 25, 2017

Answer:

#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)#