Year 7 Mathematics | Victorian Curriculum 2.0
Volume & capacity
Topic 08 | Measurement & Space | Answer key

Year 7 core - answers

Fluency

Unit conversions

    1. 2.52.5 L
    2. 46004600 mL
    3. 75007500 mL
    4. 30003000 L
    5. 4.54.5 cm^3
    6. 20002000 cm^3
Fluency

Rectangular prism

    1. 120120 cm^3
    2. 343343 cm^3
    3. 288288 m^3
    4. 20 00020\,000 cm^3 =20= 20 L
    5. 55 cm
    6. 240240 L. Method: V=240 000V = 240\,000 cm^3 =240= 240 L.
Fluency

Triangular prism

    1. 120120 cm^3. Method: base area 12×6×4=12\tfrac{1}{2} \times 6 \times 4 = 12; ×10\times 10.
    2. 3.753.75 m^3. Method: base area 1.51.5; ×2.5\times 2.5.
    3. 9696 cm^3. Method: base area 12×4×6=12\tfrac{1}{2} \times 4 \times 6 = 12; ×8\times 8.
    4. 1212 cm^2. Method: 120÷10120 \div 10.
Reasoning

Explain and reason

    1. Ben used 424^2 (the area of one face) instead of 434^3 (the volume of the cube). Volume of a cube is s3s^3: 43=644^3 = 64 cm^3.
    2. One millilitre of water fills a cube of side 11 cm - this was built into the metric system by definition.
    3. Not necessarily. Example: a 10×10×1010 \times 10 \times 10 cube and a 1×1×10001 \times 1 \times 1000 thin prism both have volume 10001000 units^3 but very different surface areas.
    4. Cube is slightly larger: 63=2166^3 = 216; prism =5×6×7=210= 5 \times 6 \times 7 = 210.
    5. Triangle area needs to be 2424 cm^2. Method: rectangular prism volume =6×4×10=240= 6 \times 4 \times 10 = 240; triangular prism volume =24×10=240= 24 \times 10 = 240.
Problem solving

Real-world problems

    1. 14401440 L. Method: V=1.2×0.8×1.5=1.44V = 1.2 \times 0.8 \times 1.5 = 1.44 m^3 =1440= 1440 L.
    2. 180180 kL; $450. Method: 15×8×1.5=18015 \times 8 \times 1.5 = 180 m^3; ×2.50\times 2.50.
    3. 10 89010\,890 cm^3 =10.89= 10.89 L.
    4. 2020 cm. Method: 36 00036\,000 cm^3 ÷(60×30)\div (60 \times 30).
    5. 1010 glasses.
    6. About 4747 cm^3. Method: triangle area ≈12×3×2.6=3.9\approx \tfrac{1}{2} \times 3 \times 2.6 = 3.9 cm^2; ×12≈46.8\times 12 \approx 46.8.
Year 7 Mathematics study companion | Answer key