7.4 Dimensional Analysis and Conversions to and from the Metric System 441 Solution a) In Table 7.7, under the heading of mass, we see that 1 pound 0.4536 kilogram. = Thus, the unit fractions we need to consider to change from pounds to kilograms are 1 lb 0.4536 kg or 0.4536 kg 1 lb We need to convert from pounds to kilograms. Thus, we need to use the unit fraction with pounds in the denominator so that the pounds will divide out. The solution follows. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = 353,000 lb 353,000 lb 0.4536 kg 1 lb 353,000(0.4536 kg) 160 120.8 kg Thus, the mass of the flagpole is 160 120.8 kilograms. b) In Table 7.7, under the heading of volume, we see that = 1 cubic yard 0.7646 cubic meter. Thus, the unit fractions we need to consider to change from cubic yards to cubic meters are 1 yd 0.7646 m or 0.7646 m 1 yd 3 3 3 3 We need to convert from cubic yards to cubic meters. Thus, we need to use the unit fraction with cubic yards in the denominator so that cubic yards will divide out. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = 700 yd 700 yd 0.7646 m 1yd 700 (0.7646 m ) 535.22 m 3 3 3 3 3 3 Thus, the volume of the concrete used is 535.22 cubic meters. c) We need to change from feet to meters. Table 7.7 shows that = 1 foot 0.3048 meter. We convert 400 feet to meters as follows. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = 400 ft 400 ft 0.3048 m 1 ft 400(0.3048 m) 121.92 m Thus, the height of the flagpole is 121.92 meters. d) To convert from square meters to square feet we need to consider the unit fractions below. 1 ft 0.0929 m or 0.0929 m 1 ft 2 2 2 2 Since we are starting with square meters, the unit fraction must have square meters in the denominator. The solution follows. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 648 m 648 m 1 ft 0.0929m 648 0.0929 ft 6975.24 ft 2 2 2 2 2 2 è Thus, the area of the flag is approximately 6975.24 square feet. e) To change from 1900 liters to gallons we do the following. 1900 1900 1 gal 3.7854 1900 3.7854 gal 501.93 gal = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = è Thus, the volume of paint used to paint the flagpole was approximately 501.93 gallons. 7 Now try Exercise 35 MATHEMATICS TODAY Metrics in Space Most of the countries on Earth use the metric system, and now the moon and the International Space Station (ISS) do, too! Recently, NASA and 13 other international space agencies decided to use the metric system for all space exploration programs. All the agencies agreed that using a single measurement system would make coordination in space, and especially on the ISS, easier. Also, standardization will make it easier for the international space agencies to collaborate and form new partnerships. Why This Is Important When countries collaborate on a scientific mission, such as the International Space Station, they must all use the same units of measurement. The common units of measure agreed upon for use on the International Space Station, and other scientific areas, are those of the metric system. m International Space Station Andrey Armyagov/ Alamy Stock Photo KDK70/Shutterstock
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