Explore · partial tank capacity
A tank has internal base 37 cm by 24 cm and is 17 cm tall. Water fills 5 cm of its height. Find water capacity in mL and empty capacity in mL.
Great Inheritance Mathematics Term A · Independent learning
Volume and Capacity — Part 2
Learning target: Solve multistep container-filling questions by relating internal Course to capacity.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
A tank fits 40 liters but contains 15 liters. How many more liters fit?
Understand the idea
Solve multistep container-filling questions by relating internal Course to capacity.
A rectangular tank’s internal Course determine full capacity. If the tank is only partly filled, substitute water height rather than tank height to find the liquid volume. Subtract from the full volume for unused capacity; convert cm³ to mL and L with care.
Vocabulary focus: unit cube, cuboid, cubic units, capacity. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Ignoring unused capacity or confusing L with mL.
Model to study: Dimensioned tank and liquid-level model.
Worked examples
Worked examples 1 · partial tank capacity
A tank has internal base 32 cm by 24 cm and is 18 cm tall. Water fills 16 cm of its height. Find water capacity in mL and empty capacity in mL.
Solution: 12,288 mL of water; 1,536 mL empty
Why: Water volume 32×24×16=12,288 cm³=12,288 mL. Full capacity 32×24×18=13,824 mL. Empty 13,824−12,288=1,536 mL.
Worked examples 2 · partial tank capacity
A tank has internal base 30 cm by 24 cm and is 14 cm tall. Water fills 5 cm of its height. Find water capacity in mL and empty capacity in mL.
Solution: 3,600 mL of water; 6,480 mL empty
Why: Water volume 30×24×5=3,600 cm³=3,600 mL. Full capacity 30×24×14=10,080 mL. Empty 10,080−3,600=6,480 mL.
Worked examples 3 · partial tank capacity
A tank has internal base 30 cm by 15 cm and is 20 cm tall. Water fills 12 cm of its height. Find water capacity in mL and empty capacity in mL.
Solution: 5,400 mL of water; 3,600 mL empty
Why: Water volume 30×15×12=5,400 cm³=5,400 mL. Full capacity 30×15×20=9,000 mL. Empty 9,000−5,400=3,600 mL.
Check understanding
Check understanding 1 · partial tank capacity
A tank has internal base 24 cm by 13 cm and is 12 cm tall. Water fills 2 cm of its height. Find water capacity in mL and empty capacity in mL.
Check understanding 2 · partial tank capacity
A tank has internal base 29 cm by 19 cm and is 14 cm tall. Water fills 1 cm of its height. Find water capacity in mL and empty capacity in mL.
Guided practice
Guided practice 1 · partial tank capacity
A tank has internal base 28 cm by 11 cm and is 17 cm tall. Water fills 16 cm of its height. Find water capacity in mL and empty capacity in mL.
Guided practice 2 · partial tank capacity
A tank has internal base 36 cm by 14 cm and is 15 cm tall. Water fills 13 cm of its height. Find water capacity in mL and empty capacity in mL.
Guided practice 3 · partial tank capacity
A tank has internal base 29 cm by 10 cm and is 23 cm tall. Water fills 13 cm of its height. Find water capacity in mL and empty capacity in mL.
Independent practice
Independent practice 1 · partial tank capacity
A tank has internal base 31 cm by 16 cm and is 15 cm tall. Water fills 2 cm of its height. Find water capacity in mL and empty capacity in mL.
Independent practice 2 · partial tank capacity
A tank has internal base 37 cm by 18 cm and is 23 cm tall. Water fills 21 cm of its height. Find water capacity in mL and empty capacity in mL.
Independent practice 3 · partial tank capacity
A tank has internal base 40 cm by 10 cm and is 12 cm tall. Water fills 5 cm of its height. Find water capacity in mL and empty capacity in mL.
Independent practice 4 · partial tank capacity
A tank has internal base 30 cm by 14 cm and is 10 cm tall. Water fills 1 cm of its height. Find water capacity in mL and empty capacity in mL.
Independent practice 5 · partial tank capacity
A tank has internal base 40 cm by 24 cm and is 12 cm tall. Water fills 9 cm of its height. Find water capacity in mL and empty capacity in mL.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “Water volume=34×12×20=8160 mL, even though water height is only 7 cm.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: A tank has internal base 34 cm by 12 cm and is 20 cm tall. Water fills 7 cm of its height. Find water capacity in mL and empty capacity in mL.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). A tank has internal base 23 cm by 10 cm and is 24 cm tall. Water fills 14 cm of its height. Find water capacity in mL and empty capacity in mL.
Exit check
Exit check 1 · partial tank capacity
A tank has internal base 24 cm by 14 cm and is 11 cm tall. Water fills 8 cm of its height. Find water capacity in mL and empty capacity in mL.
Exit check 2 · partial tank capacity
A tank has internal base 37 cm by 15 cm and is 20 cm tall. Water fills 14 cm of its height. Find water capacity in mL and empty capacity in mL.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.