I am doing Unit Analysis and I can not fugure out how to set the promble up on these 3. Am not great at these because there like word prombles can you please help. I just need to know how to set it up.
1.How many cubic meters are there in a cubic mile?
(1 mi = 1609.344 m.)
2.My 1967 Encyclopædia Britannica says that Lake Erie has a surface area of 9930 square miles and an average depth of 58 feet. How much water does it hold, in cubic miles? in liters?
(1 mi = 5280 ft; 1 liter = 0.001 m³, and use the answer to the previous problem.)
3.Lake Erie has a surface area of 9930 square miles. If an inch of rain falls on the lake one day, how many gallons have been added to its volume? How many liters?
(1 mi = 5280 ft; 1 ft = 12 in; 1 US gal = 231 in³; 1 US gal = 3.785 liters.)
1. (1609.344)^3 = ?
2. volume in miles = 9930 * 58/5280 = ? cubic miles
Above answer times answer to #1 = volume in meters
Volume in meters *.001 = ? liters
I'll leave the last one for you. Use similar processes that were used in the first two problems.
Thank you but I need to know how to write them out, I have tryed many different ways but when I cross it doesn't come out right. I know what the answer is I just need to know how to get them. So do I write it out like this.
1609.344/1 X 1/1609.344 x 1/1609.344
Sure! I can help you set up the problems using unit analysis.
1. To find how many cubic meters are in a cubic mile, we can set up a conversion factor. We know that 1 mile is equal to 1609.344 meters. Since we are dealing with cubic measurements, we need to cube the conversion factor as well.
So, the conversion factor for cubic miles to cubic meters is:
1 mi³ = (1609.344 m)³
2. To determine how much water Lake Erie holds, we need to find the volume in cubic miles and then convert it to liters. We already have the surface area in square miles and the average depth in feet.
First, let's convert the surface area from square miles to square feet:
1 mi² = (5280 ft)²
Next, we can use the average depth in feet to find the volume in cubic miles:
Volume = Surface Area * Depth
Once we have the volume in cubic miles, we can convert it to liters. We can use the conversion factor from problem 1 to convert cubic miles to cubic meters, and then convert cubic meters to liters.
3. To find how many gallons and liters have been added to Lake Erie's volume when an inch of rain falls on the lake, we need to consider the surface area of the lake and the depth of the rain.
Given:
- Surface area of Lake Erie: 9930 square miles
- Depth of rain: 1 inch
First, convert the surface area from square miles to square feet:
1 mi² = (5280 ft)²
Then, convert the depth of rain from inches to feet:
1 ft = 12 in
Next, we can calculate the volume of the rain in cubic feet:
Volume = Surface Area * Depth
Once we have the volume in cubic feet, we can convert it to gallons and liters. We can use the conversion factors provided:
1 US gal = 231 in³
1 US gal = 3.785 liters
I hope this helps you set up the problems. Let me know if you have any further questions!