# Question #b3fdb

##### 1 Answer

#### 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 thelengthof the rectangular prism#h# is itsheight#w# is itswidth

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.