Name _________________________________Date__________________ Period_____
Dimensional Analysis Practice Problems: To receive credit, do each problem using dimensional
analysis. Show all steps, label all units in each step, and cross out units that cancel.
1. The kitchen staff at MIHS wants to know how much sugar to buy to make cookies for 1500 MIHS
students. Each student will eat about 0.2 pounds of cookies.
Conversion: 1 lb sugar will make 5 lb of cookies
1500 students x
1
_______________
x _______________ =
lb sugar
2. You have $3,000 to spend on a 16 day vacation in Italy. How many Euros per day can you spend?
Conversions: 1 Euro = $1.28
$3,000
1 vacation
x
________________ x
________________ =
Euros/day
3. On average, how many pounds of carbon will the average Ford car put into the atmosphere during its
lifetime, assuming the car is driven 10,000 miles per year and lasts 12 years? The car’s gas mileage is
25 mi/gal.
Conversion: each gallon of gas will put about 4 pounds of carbon into the atmosphere.
10,000 mi
1 year
x ___________ x ___________ x ____________ =
4. How many families can live comfortably on a 1,000 mi2 island? The average family size is 4 people, and
the American standard is that each person needs 25.4 acres to live.
Conversion: 640 acres = 1 square mile
5. What is the density of water in pounds/gal? The density of water in metric units is 1 g/ml.
Conversions:
1 lb = 454 g
1 fluid ounce = 29.6 ml
1 gallon = 128 fluid ounces
6. A Pacific Giant Kelp grows at a rate of 18 inches/day. What is the rate of growth in cm/hr?
Conversions: 1 inch = 2.52 cm
7. Calculate the amount of water required to produce 1 pound of corn given the following information:


4,000 gallons of water are used per bushel of corn.
There are 70 lb. of corn per bushel.
8. To produce a pound of beef, the amount of corn required to feed the cow ranges from 6 to 20
pounds. Determine the range for the water requirements to produce a pound of beef, given the water
requirements to grow the corn that you determined in the previous question.
9. The Earth’s surface is 197 million mi2. If all of this land was available for use, what would be
population density of the Earth given that there are currently 7.17 billion people. Give your answer in
people per square mile.
10. Not all of the land can be used to support the needs of the human population. Of the 197 million
mi2, 140 million square miles are covered by water and 24.7 million square miles are marginally
productive or unproductive. What is the amount of arable (able to grow crops) is available on Earth?
What is the population density of the Earth’s inhabitants on this arable land?
11. An ecological footprint is the estimate of how much of the Earth’s area is required to meet the
needs and support the lifestyle of a person. This value includes farmland, forests, mines, dumps,
schools, hospitals, roads, malls etc. The ecological footprint for the average American is 25.4 acres (10.3
hectares). If all of the Earth’s 7 billion inhabitants lived like Americans, how much area would be
needed? Give your answer in acres and mi2 (640 acres= 1 mi2). How many planets with the same
amount of arable land as Earth would be required?
12. The ecological footprint of the average Pakistani citizen is 1.98 acres. If all of the Earth’s 7.17 billion
inhabitants lived like Pakistanis, how much area would be needed? Give your answer in acres and mi2
(640 acres= 1 mi2). How many planets with the same amount of arable land as Earth would be required?