Topic Review — Volume of Prisms — Solutions

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1. Volume units and conversion

   1. 5.2 m³ to cm³: 5 200 000 cm³
   2. 3 500 000 cm³ to m³: 3.5 m³
   3. 4500 mL to L: 4.5 L
   4. 2.8 L to mL: 2800 mL
   5. 7 L to cm³: 7000 cm³
   6. 12 000 cm³ in litres: 12 L
   7. 0.045 m³ to litres: 45 L
   8. 1.5 km³ to m³: 1.5 × 10⁹ m³

2. Volume of prisms

   1. Rectangular prism 8×5×3: V = 8 × 5 × 3 = 120 cm³
   2. Triangular prism: A = ½ × 6 × 4 = 12 cm². V = 12 × 10 = 120 cm³
   3. Cube side 7 cm: V = 7³ = 343 cm³
   4. Trapezoidal prism: A = ½(5+9)×4 = 28 cm². V = 28 × 12 = 336 cm³
   5. Height of prism: h = 360 ÷ (12×6) = 5 cm
   6. Equilateral triangular prism: V = 15.6 × 20 = 312 cm³

3. Volume applications

   1. Fish tank full: V = 60×30×40 = 72 000 cm³ = 72 L
   2. Fish tank 75%: 0.75 × 72 = 54 L
   3. Tent volume: A = ½ × 3 × 2 = 3 m². V = 3 × 5 = 15 m³
   4. Swimming pool: V = 25×10×1.5 = 375 m³ = 375 000 L
   5. Chocolate bar: A = ½ × 4 × 3 = 6 cm². V = 6 × 15 = 90 cm³

4. Problem solving with volume

   1. Packing cubes: Box V = 20×15×10 = 3000 cm³. Cube V = 2.5³ = 15.625 cm³. Number = 3000 ÷ 15.625 = 192 cubes
   2. Concrete path:
      1. V = 15 × 1.2 × 0.1 = 1.8 m³
      2. Cost = 1.8 × $180 = $324
   3. Storage container:
      1. A = ½ × 2.4 × 1.8 = 2.16 m². V = 2.16 × 6 = 12.96 m³
      2. 12.96 m³ = 12 960 L
      3. 0.60 × 12.96 = 7.776 m³
   4. Two containers: Container A: V = 10² × h = 1200, h = 12 cm. Container B: A = ½ × 8 × 8 = 32 cm². Length = 1200 ÷ 32 = 37.5 cm