I am doing Unit Analysis and I can not fugure out how to set the promble up on these 3. I just need to know how to set it up I can figure out the answer.
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.)
for #1,
1 mi = 1609.344 m
since we need units in cubic meters, we raise both sides by 3:
(1 mi)^3 = (1609.344 m)^3
1 mi^3 = 4168181825.44 m^3
for #2,
we first convert the 58 ft into miles. we use ration and proportion (let n = unknown):
1 mi : 5280 ft = n mi : 58 ft
thus
1/5280 = n/58
n = 58/5280 = 0.010985 mi
since volume is Area*height,
9930*0.010985 = 109.0795 mi^3
then we convert this into meters. from the answer we got from #1,
1 mi^3 : 4168181825.44 m^3 = 109.0795 mi^3 : n
thus
1/4168181825.44 = 109.0795/n
n = 4168181825.44*109.0795
n = 454663378890.89 m^3
finally, we convert this to L:
1 L : 0.001 m^3 = n / 454663378890.89
thus
n = 454663378890890 m^3 , or in scientific notation,
n = 4.547 x 10^14 m^3
for #3,
you do the same like in #1 and #2
hope this helps~ :)
1. To set up the problem, you need to convert the cubic mile to cubic meters. Since we know that 1 mile is equal to 1609.344 meters, we need to cube that conversion factor. So the setup would be:
1 mi^3 = (1609.344 m)^3
2. To determine how much water Lake Erie holds, we first need to calculate its volume. The formula for volume is V = A * D, where V is the volume, A is the surface area, and D is the average depth. We know that the surface area is 9930 square miles, but we need to convert it to square meters. We also know the average depth is 58 feet, which needs to be converted to meters. Once we have the volume in cubic meters, we can then convert it to cubic miles and liters using the conversions given in the problem.
V in cubic meters = (9930 mi^2 * (1609.344 m)^2) * (58 ft * 0.3048 m/ft)
3. To calculate the amount of rain that falls on Lake Erie, we need to know the volume of water added. Since we are given an inch of rain, we need to convert that to feet and then to meters. Once we have the volume in cubic meters, we can convert it to gallons and liters using the conversions provided in the problem.
Volume in cubic meters = (9930 mi^2 * (1609.344 m)^2) * (1 in * 0.0254 m/in)
I hope this helps! Please let me know if you have any more questions.
To set up the given problems using unit analysis, we can start by writing down the given information and the desired unit conversions. Let's break down each problem step-by-step:
1. How many cubic meters are there in a cubic mile?
Given conversion: 1 mi = 1609.344 m
To convert from cubic miles (mi³) to cubic meters (m³), we need to multiply the number of cubic miles by the conversion factor.
Solution:
1 mi³ * (1609.344 m/mi)^3 = 1 mi³ * 4.16818183 x 10^9 m³/mi³
So, there are approximately 4.16818183 x 10^9 cubic meters in a cubic mile.
2. 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?
Given conversions:
1 mi = 5280 ft
1 liter = 0.001 m³
To find the volume, we need to multiply the surface area by the average depth.
Solution:
Volume in cubic miles:
9930 mi² * 58 ft * (1 mi/5280 ft) * (1 mi/5280 ft) * (1 mi/5280 ft) = 9930 mi² * 58 ft * (1/5280)^3 mi³/ft³ ≈ 116.92 mi³
Volume in liters:
116.92 mi³ * (4.16818183 x 10^9 m³/mi³) * (1 liter/0.001 m³) ≈ 1.9400 x 10^15 liters
So, Lake Erie holds approximately 116.92 cubic miles of water or approximately 1.9400 x 10^15 liters of water.
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?
Given conversions:
1 mi = 5280 ft
1 ft = 12 in
1 US gal = 231 in³
1 US gal = 3.785 liters
To find the volume in gallons and then in liters, we need to multiply the surface area by the height (1 inch) and then perform the necessary unit conversions.
Solution:
Volume in gallons:
9930 mi² * 1 in * 5280 ft/mi * 5280 ft/mi * 12 in/ft * (1 gal/231 in³) ≈ 8,944,356 gallons
Volume in liters:
8,944,356 gal * (3.785 liters/gal) ≈ 33,809,408 liters
So, if an inch of rain falls on Lake Erie, approximately 8,944,356 gallons or approximately 33,809,408 liters will be added to its volume.
To set up the unit analysis problems, you can use conversion factors to convert the given measurements into the desired units. Here's how you can set up each problem:
1. Convert cubic miles to cubic meters:
To convert cubic miles to cubic meters, you need to multiply the given measurement by a conversion factor. The conversion factor you'll use is 1 mile = 1609.344 meters.
Let's set it up:
cubic miles * (conversion factor: 1 mile = 1609.344 meters) = cubic meters
2. Convert surface area and depth of Lake Erie to water volume in cubic miles and liters:
To calculate the water volume in cubic miles, you'll use the formula: volume = area * depth.
First, convert the surface area from square miles to square meters using the conversion factor 1 mile = 1609.344 meters. Then, convert the average depth from feet to meters using the conversion factor 1 foot = 0.3048 meters. Finally, convert the volume from cubic meters to cubic miles using the conversion factor you found in problem 1, which is 1 cubic mile = ??? cubic meters. To convert cubic miles to liters, you'll need one additional conversion factor, 1 liter = 0.001 cubic meters.
Let's set it up for cubic miles:
volume in cubic miles = (surface area in square miles * (conversion factor: 1 mile = 1609.344 meters) * average depth in feet * (conversion factor: 1 foot = 0.3048 meters) * (conversion factor: 1 cubic mile = ??? cubic meters) = cubic miles
And for liters:
volume in liters = (volume in cubic miles * (conversion factor: 1 cubic mile = ??? cubic meters) * (conversion factor: 1 liter = 0.001 cubic meters) = liters
3. Calculate the volume of rainwater added to Lake Erie in gallons and liters:
First, convert the surface area from square miles to square feet using the conversion factor 1 mile = 5280 feet. Then, convert the rainfall from inches to feet using the conversion factor 1 inch = 1/12 feet. Finally, convert the volume from cubic feet to gallons using the conversion factor 1 US gallon = 231 cubic inches, and then convert gallons to liters using the conversion factor 1 US gallon = 3.785 liters.
Let's set it up for gallons:
volume in gallons = (surface area in square miles * (conversion factor: 1 mile = 5280 feet) * rainfall in inches * (conversion factor: 1 inch = 1/12 feet) * (conversion factor: 1 US gallon = 231 cubic inches) = gallons
And for liters:
volume in liters = (volume in gallons * (conversion factor: 1 US gallon = 3.785 liters) = liters
By setting up the problems in this way, you can easily substitute the known values into the equations and calculate the answers.