A sample of iron that has density of 7.833 g/mL has a mass of 94 g. If the sample is in the shape of a rectangular cube, what is the height of the cube if the top is 2 cm x 3 cm?

1 Answer
Aug 30, 2017

Answer:

#"1 cm"#

Explanation:

You know that the sample is shaped as a rectangular cube, i.e. a rectangular prism, which means that you can determine its volume by using the equation

#color(blue)(ul(color(black)(V = l xx w xx h)))#

Here

  • #l# is the length of the rectangular prism
  • #w# is its width
  • #h# is its height

Now, you know that iron has a density of #"7.833 g mL"^(-1)#. This means that every #"1 mL"# of iron has a mass of #"7.833 g"#.

In your case, the sample has a mass of #"94 g"#, which means that it will occupy a volume of

#94 color(red)(cancel(color(black)("g"))) * overbrace("1 mL"/(7.833 color(red)(cancel(color(black)("g")))))^(color(blue)("the density of iron")) = "12.0005 mL"#

At this point, you should know that

#"1 mL" = "1 cm"^3#

so you can say that the volume of the prism is equal to

#V = "12.0005 cm"^3#

Since you know the volume of the prism, you can rearrange the equation to solve for its height

#V = l * w * h implies h = V/(l * w)#

Plug in your values to find

#h = ("12.0005 cm"^color(red)(cancel(color(black)(3))))/(3 color(red)(cancel(color(black)("cm"))) * 2 color(red)(cancel(color(black)("cm")))) = color(darkgreen)(ul(color(black)("1 cm")))#

The answer is rounded to one significant figure, the number of sig figs you have for the length and width of the prism.