Question #b3fdb

1 Answer
Aug 26, 2017

Answer:

Here's what I got.

Explanation:

Start by calculating the volume of the cuboid by using the fact that you're dealing with a rectangular prism

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

Here

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

Now, notice that the length and the width of the cuboid are given to you in meters and the height is given to you in centimeters. When you plug in your values into the above equation, make sure to convert the length and the width of the cuboid from meters to centimeters by using the fact that

#color(blue)(ul(color(black)("1 m" = 10^2color(white)(.)"cm")))#

You will end up with

#V = overbrace(1.5 color(red)(cancel(color(black)("m"))) * (10^2color(white)(.)"cm")/(1color(red)(cancel(color(black)("m")))))^(color(blue)("length in cm")) * overbrace(0.4 color(red)(cancel(color(black)("m"))) * (10^2color(white)(.)"cm")/(1color(red)(cancel(color(black)("m")))))^(color(blue)("width in cm")) * overbrace("2.5 cm")^(color(blue)("height in cm"))#

#V = "15,000 cm"^3#

Next, use the density of the material to calculate the mass of the cuboid in grams

#"15,000" color(red)(cancel(color(black)("cm"^3))) * overbrace("7.5 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the density of the material")) = "112,500 g"#

Finally, convert the mass of the cuboid from grams to kilograms by using the fact that

#color(blue)(ul(color(black)("1 kg" = 10^3color(white)(.)"g")))#

You will have

#"112,500" color(red)(cancel(color(black)("g"))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("110 kg")))#

I'll leave the answer rounded to two sig figs, but keep in mind that you have one significant figure for the width of the cuboid.