suppose your bedroom is 18 ft long

Question

suppose your bedroom is 18 ft long and 15 ft wide, and the distance from floor to ceiling is 8 ft 6 in. You need to know the volume of the room in metric units for some scientific calculations. 

1) what is the room's volume in cubic meters? in liters?

2) what is the mass of air in the room in kilograms? In pounds?

assume the density of air is 1.2 g/L and that the room is empty of furniture.

Answer 1

Volume = L*W*H but since you have to convert it right off the start to cubic meters, convert while you multiply. 

 

Use the conversion factor of 3.28 ft/meter in your volume formula.

 

V=L*W*H   = (18ft/3.28ft/m)(15ft/3.28ft/m)(8.5ft/3.28ft/m)=2295 cubic feet/35.29cubic ft/cubic m  

 

Divide and cancel the ft units to be left with cubic meters.

 

1a) 65.03 cubic meters

 

 

then use the conversion 1 cubic meter = 1,000 liters, multiply 65.03cubic meters by 1,000 L/cubic meter

 

1b) 65030 liters  

 

Part 2

Density formula   density = mass/volume  solve for the missing information you just found volume and they give you the density of air 1.2g/L. 

 

Therefore mass = density * volume

 

1.2g/L  g for grams per liter  so it's a good thing you know how many liters are in the room from 1b

 

1.2g/L*65030 L=  78036 g    

 

then use conversion 1000g = 1 kg   to divide 78036g by 1000g/kg

 

2a) 78kg

 

then use conversion factor 2.2lbs/kg   and multiply 78 kg by 2.2lbs/kg

 

2b)  172lbs

 

 

Answer 2

1) V = (18 ft)*(15 ft)*(8.5 ft)*(2.54 cm/in)^3*(12 in/ft)^3

    = 64987162.92864 cm^3 * (1 m/100 cm)^3 = 64.98716292864 m^3

    = 64987162.92864 cm^3 * (1 L/(1000 cm^3)) = 64,987.16292864 L

 

2) M = (64,987.16292864 L)*(1.2 g/L)*(1 kg/1000g) = 77.984595514368 kg

    * (2.20462 lbs/kg) = 171.92639896288598 lbs.

Answer 3

1) V=l*w*h

    V=18*15*8.5

    V=2295 cu ft

1 cubic meter is equal to 35.28755 cubic feet

2295/35.28755=65.0371 cubic meters

1 liter equals 1 cubic decimeter

1 liter=(0.1)(0.1)(0.1)

1 liter=0.001 of a cubic meter

1000 liters=1 cubic meter

65.0371*1000=65,037.1 liters

Answer 4

Hi Dalia;

1) what is the room's volume in cubic meters? in liters?

volume=(length)(width)(height)[(0.3048 meters)/(1 foot)]

volume=(18 feet)(15 feet)(8.5 feet)[(0.3048 meters)³/(1 foot)³]

Let's first notice that the unit of feet is multiplied three times in the numerator, and the unit of foot is to the exponential of three in the denominator.  These cancel...

volume=(18 feet)(15 feet)(8.5 feet)[(0.3048 meters)³/(1 foot)³]

volume=(18)(15)(8.5)(0.3048 meters)³

Now that our units are aligned, we may calculate...

volume=699.516 meters³

 

In liters...

1,000 liters=1 meter³

volume=(699.516 meters³)[(1,000 liters)/(1 meter³)]

The unit of cubic-meters is in the numerator and denominator.  It cancels.

volume=(699.516 meters³)[(1,000 liters)/(1 meter³)]

volume=(699.516)(1,000 liters)

volume=699,516 liters

 

assume the density of air is 1.2 g/L and that the room is empty of furniture.

699,516 liters[(1.2 grams)/(1 liter)]

The unit of liters is in the numerator and denominator.  It cancels...

699,516 liters[(1.2 grams)/(1 liter)]

699,516(1.2 grams)

839,419.2 grams

 

1000 grams=1 kg

839,419.2 grams[(1 kg)/(1000 g)]

0.8394192 kilograms

0.8394192 kilograms[(2.20462 pounds)/(1 kilogram)]

The units of kilograms cancels...

1.850600356704 pounds

 

Answer 5

Vrp = V(rectangular parallelapiped) = W*L*H

 

Vrp = (15 ft)(18 ft)(8.5 ft)=2295 cubic feet (ft^3)

Vrp = 2295 ft^3*(28.3168 L/ft^3)=64,987 L  (approx)

Vrp = 64,987L (0.001 M^3/L)= 64.987 M^3

 

Mair = Volume*Density = 64,987L (1.2 g/L)=77,984.5 grams (approx)

Mair = 77.984 Kg

Mair = 77.984 Kg*(2.205 Lbs/kg) = 171.95 Lbs

 

This is a surprising result for some.  Air seems light, but 78 Kg is significant!