Volume Units and Conversion — Solutions

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1. Convert between mm³ and cm³ Fluency

   1. 5000 mm³
   2. 8 cm³
   3. 2500 mm³
   4. 3.5 cm³
   5. 400 mm³
   6. 0.75 cm³
   7. 12 000 mm³
   8. 6.25 cm³

2. Convert between cm³ and m³ Fluency

   1. 3 000 000 cm³
   2. 2 m³
   3. 500 000 cm³
   4. 0.75 m³
   5. 4 200 000 cm³
   6. 3.5 m³
   7. 250 000 cm³
   8. 0.18 m³

3. Convert between volume and capacity Fluency

   1. 250 mL
   2. 3000 cm³
   3. 1500 cm³
   4. 4.8 L
   5. 800 L
   6. 2.5 m³
   7. 600 mL
   8. 7000 cm³

4. Mixed volume unit conversion Understanding

   1. 24 cm³  (24 000 ÷ 1000)
   2. 2000 cm³  (0.002 × 1 000 000)
   3. 5 000 000 mm³  (5 L = 5000 cm³; 5000 × 1000)
   4. 9.2 m³  (9 200 000 ÷ 1 000 000)
   5. 350 cm³
   6. 1400 L  (1.4 × 1000)
   7. 48 mL  (48 000 mm³ = 48 cm³ = 48 mL)
   8. 180 000 cm³
   9. 2.75 m³
   10. 6000 mL  (0.006 m³ = 6000 cm³ = 6000 mL)

5. Most appropriate unit Understanding

   1. cm³ — a small solid object, roughly 1–2 cm per side
   2. L — swimming pool capacity is typically tens of thousands of litres
   3. m³ — large space, several metres in each dimension
   4. mL — very small capacity, just a few drops
   5. mm³ — extremely small object
   6. L — kitchen sink holds several litres
   7. m³ — a fridge is roughly 0.3–0.5 m³
   8. L or mL — water bottles are typically 500 mL or 1 L

6. Problem Solving Problem Solving

   1. 1. 112 000 cm³  (80 × 35 × 40)
      2. 112 L  (112 000 ÷ 1000)
      3. 100.8 L  (112 × 0.9)
   2. 1. 33 200 000 cm³  (33.2 × 1 000 000)
      2. 12.5 m³  (12 500 000 ÷ 1 000 000)
      3. 20.7 m³  (33.2 − 12.5)
   3. 1. 5 m³  (5000 ÷ 1000)
      2. 5 000 000 cm³  (5000 × 1000)
      3. 2000 L and 2 m³  (5000 × 0.4 = 2000; 5 × 0.4 = 2)

7. Swimming pool problem Problem Solving

   1. 25 × 12 × 1.5 = 450 m³
   2. 450 × 1 000 000 = 450 000 000 cm³
   3. 450 m³ = 450 000 L
   4. 450 000 ÷ 600 = 750 minutes = 12 hours 30 minutes

8. Comparing containers Problem Solving

   1. A = 2.4 m³ = 2 400 000 cm³. B = 2 600 000 cm³. B is larger by 200 000 cm³.
   2. Tank volume = 80 × 60 × 50 = 240 000 cm³ = 240 L. 168 ÷ 240 × 100 = 70%
   3. Trough = 150 × 40 × 50 = 300 000 cm³ = 300 L. 300 ÷ 12 = 25 buckets
   4. 1. 3 kL = 3000 L
      2. 3000 L = 3 000 000 cm³
      3. 3 000 000 cm³ = 3 m³

9. Volume, capacity and rate problems Problem Solving

   1. 3 m³ = 3000 L. 1 mm rain over 50 m² = 50 L. Depth needed = 3000 ÷ 50 = 60 mm of rain.
   2. 250 ÷ 15 = 16.67 minutes = 1000 seconds
   3. Box volume = 60 × 40 × 30 = 72 000 cm³ = 72 000 mL. Percentage = 68 400 ÷ 72 000 × 100 = 95%
   4. 4.5 kL → 4500 L → 4 500 000 cm³ → 4 500 000 × 1000 = 4 500 000 000 mm³ = 4.5 × 10⁹ mm³

10. Real-world investigation Problem Solving

    1. Path volume = 60 × 0.1 = 6 m³. One truck carries 7 m³. Yes, one truckload is enough (with 1 m³ to spare).
    2. 180 L = 180 000 cm³. Base area = 75 × 40 = 3000 cm². Height = 180 000 ÷ 3000 = 60 cm
    3. 2 km² = 2 000 000 m². 45 mm = 0.045 m. Volume = 2 000 000 × 0.045 = 90 000 m³
    4. 15 L = 15 000 mL. 15 000 ÷ 750 = 20 bottles