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Mastering Unit Conversion: Area and Volume

Learn to convert between customary and metric units of area and volume for problem-solving. Practice exercises included.

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Mastering Unit Conversion: Area and Volume

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  1. Lesson Menu Main Idea NGSSS Example 1: Convert Units of Area Example 2: Convert Units of Volume Example 3: Convert Between Systems Example 4: Convert Between Systems Example 5: Convert Units of Volume Five-Minute Check

  2. Convert units of area and volume between customary and metric systems. Main Idea/Vocabulary

  3. MA.8.G.5.1 Compare, contrast, and convert units of measure between different measurement systems (US customary or metric (SI)) and dimensions including temperature, area, volume, and derived units to solve problems. Also addresses MA.8.A.6.4 NGSSS

  4. Multiply by . Convert Units of Area Convert 12 square yards to square feet. = 12 × 3 ft × 3 ft = 108 ft2 Answer: 12 yd2 = 108 ft2 Example 1

  5. Convert 720 square inches to square feet. A. 2 ft2 B. 4 ft2 C. 5 ft2 D. 6 ft2 Example 1 CYP

  6. Multiply by . Convert Units of Volume AIR QUALITY Morgan is using an air purifier in a room that he estimates holds about 27 cubic yards of air. How many cubic feet of air will the air purifier need to clear? = 27 × 3 ft × 3 ft × 3 ft = 729 ft3 Answer: The purifier will need to clear 729 cubic feet of air. Example 2

  7. BUILDING How many cubic inches of concrete will a builder need for a rectangular patio that has a volume of 30 cubic feet? A. 2.5 in3 B. 360 in3 C. 4,320 in3 D. 51,840 in3 Example 2 CYP

  8. Multiply by . Convert Between Systems Complete the conversion. Round to the nearest hundredth if necessary.24 in2 ≈ __ cm2 ≈ 154.84 cm2 Multiply. Answer: 154.84 Example 3

  9. Complete the conversion. Round to the nearest hundredth if necessary.3 km2 ≈ __ mi2 A. 0.39 B. 1.16 C. 4.83 D. 12.50 Example 3 CYP

  10. Multiply by . Convert Between Systems Complete the conversion. Round to the nearest hundredth if necessary.90 ft3 ≈ __ m3 ≈ 2.55 m3 Multiply. Answer: 2.55 m3 Example 4

  11. Complete the conversion. Round to the nearest hundredth if necessary.5 gal3 ≈ __ L3 A. 14.33 B. 18.93 C. 54.22 D. 271.12 Example 4 CYP

  12. Convert Units of Volume SOY MILK An individual carton of soy milk is 5 centimeters wide, 9 centimeters tall, and 3 centimeters deep. How many liters of soy milk completely fill the carton? Step 1 Find the volume. V = bwh V = 5 cm • 9 cm • 3 cm V = 135 cm3 Example 5

  13. Convert Units of Volume Step 2 Find the capacity. = 0.135 L Answer: So, 0.135 liter of soy milk completely fills the carton. Example 5

  14. WATER A water trough for horses is 180 centimeters long, 75 centimeters wide, and 35 centimeters deep. How many liters of water can it hold? A. 4.725 L B. 472.5 L C. 47,250 L D. 472,500 L Example 5 CYP

  15. Complete the conversion. Round to the nearest hundredth if necessary.2,000 in2 = __ yd2 A. 1.54 B. 13.89 C. 55.56 D. 83.33 Five Minute Check 1

  16. Complete the conversion. Round to the nearest hundredth if necessary.33 km3 = __ mi3 A. 0.24 B. 4.17 C. 7.92 D. 137.46 Five Minute Check 2

  17. Complete the conversion. Round to the nearest hundredth if necessary.4,500 m3 = __ ft3 A. 35.26 B. 5,892.02 C. 18,744.79 D. 158,603.58 Five Minute Check 3

  18. Complete the conversion. Round to the nearest hundredth if necessary.450 in2 = __ ft2 A. 3.13 B. 37.50 C. 5,400 D. 64,800 Five Minute Check 4

  19. An aquarium is 90 centimeters long, 30 centimeters wide, and 45 centimeters tall. How many liters of water can the aquarium hold? A. 1.215 L B. 121.5 L C. 1,215 L D. 121,500 L Five Minute Check 5

  20. A concrete company is pouring a rectangular driveway that is 35 feet long and 15 feet wide. If the new concrete for the driveway is poured 0.5 feet deep, approximately how many cubic yards of concrete will be needed for the whole driveway? A. 58.33 B. 29.17 C. 19.44 D. 9.72 Five Minute Check 6

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