Question

A `"450. kg"` object has a density of `"1.23 g/cm"^3"`. What is its volume in `"m"^3"`?

Answer 1

The volume is `0.366 "m"^3"`.

Explanation:

The formula for density is:

`rho=M/V`,

where `rho` (pronounced "roe") is density, `M` is mass, and `V` is volume.

Known/Given:

`rho=1.23 "g/cm"^3`

`m="450. kg"`

`1 "kg"=1000 "g"`

`1 "m"^3=1xx10^6 "cm"^3"`

Unknown:

`V`

Solution: Use dimensional analysis using the known values.

`450. color(red)cancel(color(black)("kg"))xx(1000 color(red)cancel(color(black)("g")))/(1 color(red)cancel(color(black)("kg")))xx(1 color(red)cancel(color(black)("cm"^3)))/(1.23 color(red)cancel(color(black)("g")))xx(1 "m"^3)/(1xx10^6 color(red)cancel(color(black)("cm"^3")))` `=` `0.366 "m"^3"` (rounded to three significant figures)