Estimate the amount of gasoline consumed by automobiles in the USA each year (assume population of USA is 300 million). If the gasoline consumed annually can be stored in a single tank that is 0.1 km by 0.1 km at the base, what is the height of the tank? (1 US gallon is approximately 3.78 liters). Show all calculations and state all assumptions
To estimate the amount of gasoline consumed by automobiles in the USA each year, we'll need to make a few assumptions and calculations.
Assumptions:
1. The average fuel efficiency of automobiles in the USA is 25 miles per gallon.
2. The average annual mileage per vehicle is 10,000 miles.
3. The population of the USA is 300 million.
Calculation 1:
To estimate the total amount of gasoline consumed annually, we'll first calculate the total number of gallons consumed by all automobiles in the USA. We'll start by calculating the number of automobiles in the USA.
Number of automobiles in the USA = Population of the USA / Number of people per vehicle
Assuming an average of 4 people per vehicle, we have:
Number of automobiles in the USA = 300 million / 4 = 75 million automobiles
Calculation 2:
Next, we will calculate the total number of gallons consumed annually.
Total gallons consumed annually = Number of automobiles in the USA * Average annual mileage per vehicle / Average fuel efficiency
Using the values we assumed, we calculate:
Total gallons consumed annually = 75 million * 10,000 / 25 = 30 billion gallons
Calculation 3:
To estimate the height of the tank that can store this amount of gasoline, we need to convert gallons to liters and calculate the volume of the tank.
1 US gallon ≈ 3.78 liters
Volume of gasoline consumed annually = Total gallons consumed annually * 3.78 liters
Using the value we calculated, we get:
Volume of gasoline consumed annually = 30 billion * 3.78 liters
Finally, since we know the base of the tank is 0.1 km by 0.1 km, we can calculate the height of the tank using the formula:
Height of the tank (h) = Volume of gasoline consumed annually / (Base area of the tank)
Height of the tank (h) = Volume of gasoline consumed annually / (0.1 km * 0.1 km)
Now, substitute the values we calculated to find the height:
h = (30 billion * 3.78 liters) / (0.1 km * 0.1 km)
Calculating this, we find the approximate height of the tank required.