The record for the largest glass bottle was set in 1992 by a team in New Jersey- they blew a bottle wit a a volume of 193 U.S. fluid gallons.
a)How much short of 1.0 million cubic centimeters is that?
b)If the bottle were filled with water at the leisurely rate of 1.8g/min, how long would the filling take? Water has a density of 1000kg/m^3.
Are you having some difficulty with this? We will be happy to critique your work.
a) 10^6 cm^3 = 10^3 liters = 264.2 gallons
They were 264.2 - 193 = 71.2 gallons (or 26.9%) short of 10^6 cm^3. The actual volume in cm^3 is 7.31*10^5 cm^3
b) Time to fill = Volume/(fill rate)
Is the 1.8 g/min grams per minute or gallons/min? You need to know
1.8 grams/min is more like a leaky faucet.
a) To find out how much short of 1.0 million cubic centimeters the bottle is, we need to convert U.S. fluid gallons to cubic centimeters.
1 U.S. fluid gallon is equal to approximately 3,785.41 cubic centimeters.
Volume of the bottle in cubic centimeters:
193 U.S. fluid gallons * 3,785.41 cubic centimeters/U.S. fluid gallon = 729,214.3 cubic centimeters.
The amount short of 1.0 million cubic centimeters:
1,000,000 cubic centimeters - 729,214.3 cubic centimeters = 270,785.7 cubic centimeters.
Therefore, the bottle is approximately 270,785.7 cubic centimeters short of 1.0 million cubic centimeters.
b) To calculate how long it would take to fill the bottle with water, we need to convert the volume of the bottle to liters and then to cubic meters.
Volume of the bottle in liters:
193 U.S. fluid gallons * 3.78541 liters/U.S. fluid gallon = 729.2143 liters.
Volume of the bottle in cubic meters:
729.2143 liters * 0.001 cubic meters/liter = 0.7292143 cubic meters.
Next, we need to calculate the mass of the water using the density formula:
Mass = Volume * Density
Mass of the water:
0.7292143 cubic meters * 1000 kg/m^3 = 729.2143 kg.
Finally, we can calculate the filling time using the given water filling rate:
Time = Mass / Filling Rate
Filling time:
729.2143 kg / 1.8 g/min * (1 kg / 1000 g) * (60 min / 1 hour) = 729.2143 / (1.8 * 1000 * 60) hours.
Calculating the filling time will give you the answer in hours.
a) To find out how much short of 1.0 million cubic centimeters the volume of the glass bottle is, we need to convert the volume of the bottle from U.S. fluid gallons to cubic centimeters.
1 U.S. fluid gallon is equal to approximately 3785 cubic centimeters. Therefore, the volume of the glass bottle is:
193 U.S. fluid gallons * 3785 cubic centimeters/1 U.S. fluid gallon ≈ 730,305 cubic centimeters
To calculate how much short the volume is from 1.0 million cubic centimeters:
1,000,000 cubic centimeters - 730,305 cubic centimeters = 269,695 cubic centimeters
So, the volume of the glass bottle is short of 1.0 million cubic centimeters by approximately 269,695 cubic centimeters.
b) To calculate the filling time, we need to determine the mass of water in the bottle and then divide it by the filling rate.
First, we need to convert the volume of the bottle from cubic centimeters to liters because the density of water is in kilograms per cubic meter.
730,305 cubic centimeters ≈ 730.305 liters
Next, we need to determine the mass of the water using the density of water:
Mass = Volume * Density
Mass = 730.305 liters * 1000 kilograms per cubic meter
Mass ≈ 730,305 kilograms
Now, we can calculate the filling time:
Filling Time = Mass / Filling Rate
Filling Time = 730,305 kilograms / (1.8 grams per minute * (1 kilogram / 1000 grams))
Filling Time ≈ 405,170 minutes
So, if the bottle were filled with water at a leisurely rate of 1.8g/min, it would take approximately 405,170 minutes to fill.