Quick Delivery charges $0.10 per cubic inch. How much will it cost to send a package 3 cm wide, 8 cm long, and 2 cm deep?

We can do this by finding the volume for the package in #"cm"^3,# and multiplying by the shipping rate per volume. Since the shipping rate is in #"in"^3# and not #"cm"^3#, we also multiply by #color(blue)"a conversion rate".#

For package volume #V#:
#V=w times l times d#
#V=3" cm" times 8" cm" times 2" cm"#
#V=48 "cm"^3#

Let the "cost-per-volume" rate be #r#. Then #r=$0.10//"in"^3#.

For shipping cost #C#:
#C=Vtimes r#
#C=48" cm"^3times$0.10//"in"^3#
#C=48" cm"^3times$0.10//"in"^3color(blue)(times("1 in"/"2.54 cm")^3)#
#C=48 color(red)cancel("cm"^3)times($0.10)/color(navy)cancel("1 in"^3)times(color(navy)cancel("1 in"^3)/("16.387064" color(red)cancel("cm"^3)))#
#C=$0.29291...#
#Capprox$0.29#

It would cost approximately 29 cents to ship this package.

Note: it doesn't matter if you think of this as "converting the volume to cubic inches" or as "converting the shipping rate to cubic centimeters". It's all multiplication, so the math is the same.

Bonus:

We could also do it by converting each side length to inches first:
#w="3 cm"#
#w="3 cm"color(blue)(times"1 in"/"2.54 cm")#
#wapprox1.1811 " in"#

Similarly, #l approx 3.1496" in",# and #d approx 0.7874" in".#

Then
#V=w times l times d#
#V approx 1.1811" in"times3.1496" in"times0.7874" in"#
#V approx 2.9291" in"^3#

Then the cost #C# to ship this package is

#C=V times r#
#Capprox2.9291color(red)cancel(" in"^3)times ($0.10)/color(red)cancel("in"^3)#
#Capprox$0.29291#
#Capprox$0.29#