If an object has a density of #8.65# #g##/cm^3#, what is its density in units of #kg##/m^3#?
1 Answer
Explanation:
Your goal here will be to use two conversion factors, one to take you from grams to kilograms and one to take you from cubic centimeters to cubic meters.
The first conversion factor is pretty straight forward
#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 kg" = 10^3"g")color(white)(a/a)|)))#
For the second conversion factor, use the fact that
#"1 m"^3 = "1 m" xx "1 m" xx "1 m"#
Now, you will have to go from centimeter to decimeter, then from decimeter to meter by using the fact that you have
#{: ("1"color(white)(a)"m " = " 10 dm "), ("1 dm " = " 10 cm") :}} implies "1 m" = 10 xx "10 cm" = 10^2"cm"#
Therefore,
#"1 m"^3 = overbrace(10^2"cm")^(color(blue)("= 1 m")) " "xx" " overbrace(10^2"cm")^(color(blue)("= 1 m")) " "xx" " overbrace(10^2"cm")^(color(blue)("= 1 m")) #
and so
#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 m"^3 = 10^6"cm"^3)color(white)(a/a)|)))#
The given density will thus be equivalent to
#8.56 color(red)(cancel(color(black)("g")))/(color(red)(cancel(color(black)("cm"^3)))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) * (10^6color(red)(cancel(color(black)("cm"^3))))/"1 m"^3 = color(green)(|bar(ul(color(white)(a/a)color(black)(8.56 * 10^3color(white)(a)"kg m"^(-3))color(white)(a/a)|)))#
