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Homework: Square and
Cubic Conversions

Linear Measure
2.54 cm = 1 in
12 in = 1 ft
5280 ft = 1 mi
1 m = 3.281 ft
1 km = 0.621 mi
1 furlong = 660 ft
Weight/Mass
1 stone = 14 lbs
1 lb = 0.4536 kg
1 oz = 28.3 g
16 oz = 1 lb
1 metric ton = 2,000 lbs
1 metric ton = 103 kg
Volumetric Measure
1 cm3 = 1 mL
1 gal = 3.78 L
14.79 mL = 1 tbsp.
1 m3 = 103 L
1 cup = 237 mL
1 gal = 4 quarts
Time
60 s = 1 min
60 min = 1 hr
24 hr = 1 day
365 day = 1 yr
10 yr = 1 decade
100 yr = 1 century


  1. 1.2 × 10-3 m3 to cm3
  2. 11 m3 to ft3
  3. 9.40 × 10-2 ft2 to in2
  1. 6.44 × 109 m3 to mi3
  2. 5.70 × 105 km2 to mi2
  3. 1.5 × 103 ft2 to m2


  1. The Greenland ice sheet has a volume of 6.3 × 105 cubic miles. What is the volume of ice in cubic kilometers?
  2. “In 2006, estimated monthly changes in the mass of Greenland’s ice sheet suggest that it is melting at a rate of about 239 cubic kilometers per year. These measurements came from the US space agency's Grace (Gravity Recovery and Climate Experiment) satellite, launched in 2002, as reported by BBC.” What is this rate in cubic miles per year? (From the Wikipedia page about the Greenland ice sheet.)
  3. At the rate given in the previous problem how many years will it take for the whole Greenland ice sheet to melt? (This rate is likely to be variable and will depend on changes in human activity with regard to greenhouse gas emissions.)


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Challenge Problems

Apply your skill in dimensional analysis to solve these problems.

  1. You own a nice downtown apartment that you wish to advertise for rent out to foreigners. The apartment has an area of 1,500 ft2. Since most people in the world use the metric system this number will not mean much to them. Convert this number to square meters so that your advertisement will be effective.
  2. The density of silver (Ag) is 1.050 × 104 kg/m3. What is its density in g/cm3? Show your work.
  3. Use the density of alumuminm (Al) to calculate the volume of Al metal in a 1.000 square-foot piece of Al that has a mass of 3.636 g. The density of Al is 2.70 g/cm3. Hint: use the density as a conversion factor where 2.70 g = 1 cm3.
  4. Using the formula for the volume of a rectangular solid (V = L × W × H) find the thickness of the piece of foil described in the previous problem. The surface area of 1.000 ft2 represents the length times width part of the volume formula. You found the volume in cubic centimeters in the previous problem. What is the thickness of the foil in centimeters (cm)?
  5. Vanillin (used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects in the smallest amount. The threshold limit is 2.0 × 10-11 g/L of air. If the current price of 50 g of vanillin is $112, determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.0 × 107 ft3.
  6. The total volume of sea water is 1.4 × 1018 m3. Assume that sea water contains 3.1 percent sodium chloride by mass (3.1 g out of every 100 g of salt water). The density of sea water is 1.03 g/mL. Calculate the total mass of sodium chloride in kilograms.
Activity: Constructing Square and Cubic Units
Activity: Calculating with Square and Cubic Units
Last updated: Oct 21, 2013 Home