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Displacement Method for Volume Paper 3: Challenge
Displacement Method for Volume Paper 3: Challenge
Existing depths, decimal rises and floating bodies, training multi-step reasoning.
Direct answers Answers and explanations for all ten questions
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P5 Displacement Method for Volume |
| Level | P1 |
02 Questions (10 items)
- FoundationA tank 20 cm by 15 cm holds water 8 cm deep, and the depth becomes 11.5 cm after a stone is added. Find the volume of the stone.
- FoundationA stone of 360 cm cubed is put in a tank 30 cm long and 20 cm wide. How far does the level rise?
- Foundation250 cm cubed of iron and then 180 cm cubed of copper are put into 1 000 mL of water. What is the final reading?
- IntermediateThe depth in a tank of base area 250 cm squared rises from 8.4 cm to 9.6 cm. Find the volume of the object.
- IntermediateA container full to the brim holds 2 L. A stone is added and 0.35 L of water overflows. Find the volume of the stone.
- IntermediateWhy does the displacement method fail to give the full volume of an ice cube floating on water?
- ChallengeA tank 15 cm by 10 cm holds water 6 cm deep. Five steel balls of 24 cm cubed each are added. Find the new depth.
- ChallengeAn object of 900 cm cubed is put in a tank with a square base of side 15 cm. How far does the water rise?
- ChallengeThe level hardly changes when a wooden block is placed in water. How can its volume be measured by displacement?
- Error redoA tank 12 cm by 8 cm shows a rise of 5 cm. A student multiplies the perimeter 40 cm by 5 and answers 200 cm cubed. What is the correct volume?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1050.0 cm cubed, from a base area of 300 cm squared times a rise of 3.5 cm. | Find the base area and the rise first, then multiply. |
| 2 | 0.6 cm, because the base area is 600 cm squared and 360 divided by 600 gives 0.6. | When the volume is smaller than the base area, the rise is under 1 cm. |
| 3 | 1430 mL, from 1 000 plus 250 plus 180. | When everything sinks fully, the volumes simply add up. |
| 4 | 299.99999999999983 cm cubed, from a rise of 1.2 cm times 250. | Subtract decimal depths exactly; do not round them first. |
| 5 | 350 cm cubed, because 0.35 L is 350 mL and the overflow equals the volume. | Change the unit first, then read the overflow as the volume. |
| 6 | A floating body displaces only water equal to its weight, not its whole volume, so the rise is too small. Press it under with a needle or weight it down until it sinks fully. | Displacement needs the object fully submerged, so a floating body must be pushed down. |
| 7 | 6.8 cm, from a total of 120 cm cubed, a rise of 0.8 cm and the original 6 cm. | Total volume, then rise, then add the original depth. |
| 8 | 4.0 cm, because the base area is 225 cm squared and 900 divided by 225 gives 4. | The area of a square base is the side multiplied by itself. |
| 9 | Push the block fully under with a fine needle, or tie it to a weight so that it sinks, then read the rise. Multiply the rise by the base area and subtract the volume of the weight. | Make a floating body sink first, then subtract the helper volume. |
| 10 | 480 cm cubed, using a base area of 96 cm squared times 5. The 40 cm is a perimeter, not an area. | Base area is length times width, not the perimeter. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Find the rise, multiply by the base area, and press floating bodies under first.Tutor Registration →
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