Algebra Unit Analysis

Question

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.)

Jai · Accepted Answer

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~ :)

Algebra Unit Analysis

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