QuestionConvert the room volume of $47.3 \mathrm{~m}^{3}$ to liters (L), knowing that $1 \mathrm{~L} = 1 \mathrm{dm}^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The volume of the room is $47.3 \mathrm{~m}^{3}$ . We need to convert this volume to liters ()
3. The conversion factor is that $1 \mathrm{~}$ is equal to $1 \mathrm{dm}^{3}$
4. There are $1000 \mathrm{dm}^{3}$ in $1 \mathrm{m}^{3}$ (because $1 \mathrm{m} =10 \mathrm{dm}$ and we cube this conversion factor to convert between cubic meters and cubic decimeters)

STEP 2

First, we need to convert the volume from cubic meters to cubic decimeters. We can do this by multiplying the volume in cubic meters by the conversion factor.
$Volume_{dm^{}} = Volume_{m^{}} \\times Conversion\, factor$

STEP 3

Now, plug in the given values for the volume in cubic meters and the conversion factor to calculate the volume in cubic decimeters.
$Volume_{dm^{3}} =47.3 \mathrm{~m}^{3} \\times1000 \mathrm{dm}^{3}/\mathrm{m}^{3}$

STEP 4

Calculate the volume in cubic decimeters.
$Volume_{dm^{3}} =47.3 \mathrm{~m}^{3} \\times1000 \mathrm{dm}^{3}/\mathrm{m}^{3} =47300 \mathrm{~dm}^{3}$

STEP 5

Now that we have the volume in cubic decimeters, we can convert this to liters using the given conversion factor of $1 \mathrm{~} =1 \mathrm{dm}^{3}$ .
$Volume_{} = Volume_{dm^{3}}$

STEP 6

Plug in the value for the volume in cubic decimeters to calculate the volume in liters.
$Volume_{} =47300 \mathrm{~dm}^{3}$ The volume of the room is $47300 \mathrm{~}$ .

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