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Applications of Conversions

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1. You are ordering linoleum for an 18' by 15' kitchen, but when you get to the store the measurements are in square yards, how much should you order?

2. Is the following statement reasonable? (Justify your answer!) The area of a dorm room is 49 m2.

3. A round silo is 60 feet tall and has a 15 foot radius. What percentage would a load of 32,000 ft3 of grain fill the silo to? Hint - Here is the problem reworded: 32,000 is what percent of total volume?

4. A cylindrical shaped vase has a radius of 3 cm and a height of 18 cm.
How much water in L would it take to completely fill the vase?

5. What is the volume of a rectangle with the following dimensions? 15 ft by 2.3 meters by 92 inches

6. Find the volume of a cylinder with a radius of 46.8 inches and a height of 1.6 meters.

7. A person that weighs 179 lbs needs an IV drip in mL. The drug only comes in powder form but can be converted as 10 mg is equal to 2 mL. How much should the patient be given if they need at least 60 mg for each kg they weigh?

8. A certain drug dosage calls for 25 mg per kg per day and is divided into two doses (1 every 12 hours). If a person weighs 180 pounds, how much of the drug should they get each dosage?

9. If a drug has a concentration of 275 mg per 10 mL, how many mL are needed to give 1 gram of the drug?

10. If the max dose of a drug required is 90 mg/kg each day, how much should a person that weighs 205 lbs get each week total?

11. The gas tank of a 2012 Toyota Prius holds 11.9 gallons. How many pounds of carbon dioxide are produced by burning an entire tank of gas?

12. The Honda CR-Z gets 37 miles per gallon on average. How much carbon dioxide would be emitted if the Honda were driven 400 miles?

13. If a truck gets 14 mile to the gallon on average, how much carbon dioxide is emitted into the atmosphere when the truck travels 200 miles?

14. A PS4 uses 8.8 watts when on stand-by mode.
A. How many kWh would be used if you have your PS4 on standby 24 hours a day for 1 week?
B. How much carbon dioxide is emitted into the atmosphere by using this electricity?
C. If electricity in your area costs $0.10 per KWH, how much would this cost?

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Solution Summary

Step-by-step computations are shown for each problem showing the conversions of different measurements.

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1
1 yard = 3 feet
18 / 3 = 6
15 / 3 = 5
6 * 5 = 30
Order 30 square yards

2
49 m2 is close to 49 square yards. The room is approximately 7 yards by 7 yards, or 21 feet by 21 feet. This is reasonable.

3
We will assume the silo is cylindrical.
Total volume of silo = 3.14 * (15^2) * 60 = 42390
32000 / 42390 * 100 = 75.5
The percentage is 75.5%

4
Volume of vase = 3.14 * (3^2) * 18 = 508.68 cubic cm
1000 cubic cm = 1 L
508.68 / 1000 = 0.50868
It would take 0.50868 L

5
Convert all dimensions to feet.
1 meter = 3.28084 feet
2.3 * 3.28084 = 7.545932 feet
12 inches = 1 foot
92 / 12 = 7.666667 ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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