Year 8 Mathematics | Victorian Curriculum 2.0
Volume of right prisms
Topic 09 | Measurement & Space | Answer key

Year 8 core - answers

Fluency

Volume of right prisms

    1. 8484 cm3^3
    2. 216216 cm3^3
    3. 450450 cm3^3. Method: triangle area 3030; × 1515.
    4. 120120 m3^3. Method: trapezium area 12(4+6)×3=15\tfrac{1}{2}(4+6) \times 3 = 15; × 88.
    5. 1212 cm. Method: 480÷40480 \div 40.
    6. 1515 cm2^2. Method: 150÷10150 \div 10.
Fluency

Volume and capacity

    1. 3.53.5 L
    2. 42004200 mL
    3. 750750 L
    4. 23002300 mL
    5. 7272 L. Method: V=72 000V = 72\,000 cm3=72^3 = 72 L.
    6. 108108 kL. Method: V=108V = 108 m3^3.
Fluency

Rates and time

    1. 6060 min =1= 1 h.
    2. 55 min. Method: 0.20.2 L/s =12= 12 L/min; 60÷1260 \div 12.
    3. 1010 hours. Method: 90 000÷150=60090\,000 \div 150 = 600 min.
    4. About 17.317.3 L/day. Method: 4×86 400=345 6004 \times 86\,400 = 345\,600 drops/day; ÷20=17 280\div 20 = 17\,280 mL.
Reasoning

Explain and spot the mistake

    1. 88 is correct numerically but the units should be cm3^3 (cube has volume in cubic units). cm2^2 is area.
    2. Not necessarily. Example: 1×1×10001 \times 1 \times 1000 and 10×10×1010 \times 10 \times 10 both have volume 10001000 but very different surface areas.
    3. The metric system was built so that 11 cm3^3 holds exactly 11 mL of water. They are different units measuring the same amount of space or liquid.
    4. Over 11 hour? 1212 L/min × 6060 = 720720 L in an hour - only 720720 of 10001000 L. So it takes over 11 hour.
Problem solving

Real contexts

    1. 7272 min. Method: V=1.44V = 1.44 m3=1440^3 = 1440 L; 1440÷201440 \div 20.
    2. $403.20. Method: V=15×8×1.4=168V = 15 \times 8 \times 1.4 = 168 m3^3 = 168168 kL; × 2.402.40.
    3. 10 89010\,890 cm3=10.89^3 = 10.89 L.
    4. 3939 cm3^3. Method: triangle area 12×3×2.6=3.9\tfrac{1}{2} \times 3 \times 2.6 = 3.9; × 10=3910 = 39.

Challenge - answers

Reasoning

Harder problems

    1. 125125 cm3^3. Method: 6s2=1506 s^2 = 150, so s2=25s^2 = 25, s=5s = 5; V=53V = 5^3.
    2. 120120 cm3^3. Method: two prisms combine so half of the cuboid; each triangle area 66; cuboid =4×3×10=120= 4 \times 3 \times 10 = 120.
    3. 133.3133.3 min (about 22 h 1313 min). Method: V=2V = 2 m3=2000^3 = 2000 L; net fill rate =15= 15 L/min; 2000÷152000 \div 15.
    4. 282.6282.6 mL (approx). Method: V=π×9×10≈282.6V = \pi \times 9 \times 10 \approx 282.6 cm3^3.
Year 8 Mathematics study companion | Answer key