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

Studdy Solution

STEP 1

Assumptions1. The volume of the room is $47.3 \, m^{3}$ . The definition of $1 \, L$ is $1 \, dm^{3}$
3. The conversion factor from $m^{3}$ to $dm^{3}$ is $1 \, m^{3} =1000 \, dm^{3}$

STEP 2

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

STEP 3

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

STEP 4

Calculate the volume in $dm^{3}$ .
$Volume_{dm^{3}} =47.3 \, m^{3} \times1000 \, dm^{3}/m^{3} =47300 \, dm^{3}$

STEP 5

Now that we have the volume in $dm^{3}$ , we can convert this to liters using the definition of $1 \, L =1 \, dm^{3}$ .
$Volume_{} = Volume_{dm^{3}}$

STEP 6

Plug in the value for the volume in $dm^{3}$ to calculate the volume in liters.
$Volume_{} =47300 \, dm^{3}$

STEP 7

The volume in liters is the same as the volume in $dm^{3}$ .
$Volume_{} =47300 \, L$ The volume of the room is $47300 \, L$ .

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

Studdy Solution

STEP 1

Assumptions1. The volume of the room is $47.3 \, m^{3}$ . The definition of $1 \, L$ is $1 \, dm^{3}$
3. The conversion factor from $m^{3}$ to $dm^{3}$ is $1 \, m^{3} =1000 \, dm^{3}$

STEP 2

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

STEP 3

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

STEP 4

Calculate the volume in $dm^{3}$ .
$Volume_{dm^{3}} =47.3 \, m^{3} \times1000 \, dm^{3}/m^{3} =47300 \, dm^{3}$

STEP 5

Now that we have the volume in $dm^{3}$ , we can convert this to liters using the definition of $1 \, L =1 \, dm^{3}$ .
$Volume_{} = Volume_{dm^{3}}$

STEP 6

Plug in the value for the volume in $dm^{3}$ to calculate the volume in liters.
$Volume_{} =47300 \, dm^{3}$

STEP 7

The volume in liters is the same as the volume in $dm^{3}$ .
$Volume_{} =47300 \, L$ The volume of the room is $47300 \, L$ .

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QuestionConvert a room volume of 47.3 m347.3 \mathrm{~m}^{3}47.3 m3 to liters (L\mathrm{L}L), knowing 1 L=1dm31 \mathrm{~L} = 1 \mathrm{dm}^{3}1 L=1dm3.

Studdy Solution

STEP 1

Assumptions1. The volume of the room is 47.3 m347.3 \, m^{3}47.3m3 . The definition of 1 L1 \, L1L is 1 dm31 \, dm^{3}1dm33. The conversion factor from m3m^{3}m3 to dm3dm^{3}dm3 is 1 m3=1000 dm31 \, m^{3} =1000 \, dm^{3}1m3=1000dm3

STEP 2

First, we need to convert the volume from mm^{}m to dmdm^{}dm. We can do this by multiplying the volume in mm^{}m by the conversion factor.Volumedm=Volumem×Conversion factorVolume_{dm^{}} = Volume_{m^{}} \times Conversion\, factorVolumedm​=Volumem​×Conversionfactor

STEP 3

Now, plug in the given values for the volume in m3m^{3}m3 and the conversion factor to calculate the volume in dm3dm^{3}dm3.Volumedm3=47.3 m3×1000 dm3/m3Volume_{dm^{3}} =47.3 \, m^{3} \times1000 \, dm^{3}/m^{3}Volumedm3​=47.3m3×1000dm3/m3

STEP 4

Calculate the volume in dm3dm^{3}dm3.Volumedm3=47.3 m3×1000 dm3/m3=47300 dm3Volume_{dm^{3}} =47.3 \, m^{3} \times1000 \, dm^{3}/m^{3} =47300 \, dm^{3}Volumedm3​=47.3m3×1000dm3/m3=47300dm3

STEP 5

Now that we have the volume in dm3dm^{3}dm3, we can convert this to liters using the definition of 1 L=1 dm31 \, L =1 \, dm^{3}1L=1dm3.Volume=Volumedm3Volume_{} = Volume_{dm^{3}}Volume​=Volumedm3​

STEP 6

Plug in the value for the volume in dm3dm^{3}dm3 to calculate the volume in liters.Volume=47300 dm3Volume_{} =47300 \, dm^{3}Volume​=47300dm3

STEP 7

The volume in liters is the same as the volume in dm3dm^{3}dm3.Volume=47300 LVolume_{} =47300 \, LVolume​=47300LThe volume of the room is 47300 L47300 \, L47300L.

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

Assumptions1. The volume of the room is $47.3 \, m^{3}$ . The definition of $1 \, L$ is $1 \, dm^{3}$
3. The conversion factor from $m^{3}$ to $dm^{3}$ is $1 \, m^{3} =1000 \, dm^{3}$

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

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

Calculate the volume in $dm^{3}$ .
$Volume_{dm^{3}} =47.3 \, m^{3} \times1000 \, dm^{3}/m^{3} =47300 \, dm^{3}$

Now that we have the volume in $dm^{3}$ , we can convert this to liters using the definition of $1 \, L =1 \, dm^{3}$ .
$Volume_{} = Volume_{dm^{3}}$

Plug in the value for the volume in $dm^{3}$ to calculate the volume in liters.
$Volume_{} =47300 \, dm^{3}$

The volume in liters is the same as the volume in $dm^{3}$ .
$Volume_{} =47300 \, L$ The volume of the room is $47300 \, L$ .