Grade 8 Unit Mastery Quiz

This quiz assesses the unit Volume Units and Reasonableness Checks in Grade 8 geometry and measurement. It assumes the learner has already studied the linked lesson and completed guided practice.

For instruction and concept-building, use:

• [rea.m08.geometry-measurement.volume.basic-formulas.units-reasonableness.lesson]
• [rea.m08.geometry-measurement.volume.basic-formulas.units-reasonableness.practice-set]
• [rea.m08.geometry-measurement.volume.basic-formulas.units-reasonableness]

This record is for assessment: ten questions, full marking solutions, and a mastery recommendation.

Quiz Directions

• Show all work.
• Write every final volume with units.
• Use pi ≈ 3.14 unless told otherwise.
• If a question asks whether an answer is reasonable, give a short justification.

Marking and Mastery

• Total: 20 marks
• Suggested weighting: most questions are 2 marks each.
• Recommended mastery threshold: 16/20 (80%), with at least:
  • one successful rectangular-prism reasonableness check,
  • one successful cylinder units check,
  • no repeated error of writing area units (cm^2) or linear units (cm) instead of cubic units (cm^3).

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Question 1

A right rectangular prism has length 8 cm, width 3 cm, and height 5 cm.

1. Find its volume.
2. Write the answer with the correct unit.

Solution

Use V = lwh.

V = 8 x 3 x 5 = 120

So the volume is 120 cm^3.

Marking

• 1 mark: correct multiplication using prism dimensions
• 1 mark: correct final unit cm^3

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Question 2

A box has dimensions 2.5 m, 4 m, and 1.2 m. A student says the volume is 12 m^2.

1. Find the correct volume.
2. Explain what is wrong with the student's answer.

Solution

Use V = lwh.

V = 2.5 x 4 x 1.2 = 10 x 1.2 = 12

So the correct volume is 12 m^3.

The number 12 is correct, but the unit is wrong. Volume must be written in cubic units, so m^2 is an area unit, not a volume unit.

Marking

• 1 mark: correct volume value 12
• 1 mark: explains that m^2 is incorrect and m^3 is required

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Question 3

A cylinder has radius 4 cm and height 10 cm. Find its volume. Use pi ≈ 3.14.

Solution

Use V = pi r^2 h.

V = 3.14 x 4^2 x 10 = 3.14 x 16 x 10 = 3.14 x 160 = 502.4

So the volume is 502.4 cm^3.

Marking

• 1 mark: correct substitution into pi r^2 h
• 1 mark: correct final answer 502.4 cm^3

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Question 4

A cylindrical can has radius 3 cm and height 12 cm. One student claims its volume is 339.12 cm^3. Another student claims its volume is 113.04 cm^3.

Which answer is correct? Show why.

Solution

Use V = pi r^2 h with pi ≈ 3.14.

V = 3.14 x 3^2 x 12 = 3.14 x 9 x 12 = 3.14 x 108 = 339.12

So 339.12 cm^3 is correct.

The answer 113.04 cm^3 comes from using 3.14 x 3 x 12, which forgets to square the radius.

Marking

• 1 mark: identifies 339.12 cm^3 as correct
• 1 mark: shows or explains that the incorrect answer failed to use r^2

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Question 5

A rectangular fish tank is 40 cm long, 25 cm wide, and 30 cm high. A student says the volume is 300 000 cm^3.

Is this answer reasonable? Find the correct volume and explain.

Solution

Compute the volume:

V = 40 x 25 x 30 = 1000 x 30 = 30 000

The correct volume is 30 000 cm^3.

The student's answer is not reasonable because it is 10 times too large. Since 40 x 25 = 1000, multiplying by 30 should give 30 000, not 300 000.

Marking

• 1 mark: correct volume 30 000 cm^3
• 1 mark: clear reasonableness explanation

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Question 6

A gift box has volume 96 cm^3. Its length is 8 cm and width is 4 cm. Find the height.

Solution

Use V = lwh.

96 = 8 x 4 x h 96 = 32h h = 96 / 32 = 3

So the height is 3 cm.

Reasonableness check: 8 x 4 x 3 = 96, so the answer fits.

Marking

• 1 mark: correct equation or division process
• 1 mark: correct height 3 cm

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Question 7

A cylinder has volume 615.44 cm^3, radius 7 cm, and height 4 cm. Is this volume reasonable? Use pi ≈ 3.14.

Solution

Check by calculating:

V = pi r^2 h = 3.14 x 7^2 x 4 = 3.14 x 49 x 4 = 3.14 x 196 = 615.44

Yes, the volume is reasonable because it exactly matches the formula result.

Marking

• 1 mark: correct check using the cylinder formula
• 1 mark: justified conclusion that the value is reasonable

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Question 8

A storage bin measures 0.6 m by 0.5 m by 0.4 m.

1. Find the volume in cubic metres.
2. A student writes 0.12 m^3 and says, "That seems too small to be a volume." Is the student correct?

Solution

V = lwh

V = 0.6 x 0.5 x 0.4 = 0.3 x 0.4 = 0.12

So the volume is 0.12 m^3.

The student is not correct. A volume can be less than 1 m^3. Since each dimension is less than 1 m, the volume should also be less than 1 m^3. So 0.12 m^3 is reasonable.

Marking

• 1 mark: correct volume 0.12 m^3
• 1 mark: explains why a decimal cubic-metre answer can still be reasonable

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Question 9

A right rectangular prism and a cylinder are shown below.

• Prism: 9 cm x 2 cm x 6 cm
• Cylinder: radius 3 cm, height 4 cm

Which solid has the greater volume? Show both calculations.

Solution

Prism:

V = lwh = 9 x 2 x 6 = 108 cm^3

Cylinder:

V = pi r^2 h = 3.14 x 3^2 x 4 = 3.14 x 9 x 4 = 3.14 x 36 = 113.04 cm^3

Compare:

• Prism: 108 cm^3
• Cylinder: 113.04 cm^3

The cylinder has the greater volume.

Marking

• 1 mark: correct prism volume
• 1 mark: correct cylinder volume and comparison conclusion

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Question 10

A student solves a cylinder problem like this:

V = pi r^2 h = 3.14 x 5^2 x 8 = 628 cm^2

Find both mistakes and give the correct final answer.

Solution

First calculate the correct volume:

V = 3.14 x 5^2 x 8 = 3.14 x 25 x 8 = 3.14 x 200 = 628

So the correct volume is 628 cm^3.

There are two issues to notice:

1. The final unit should be cm^3, not cm^2, because volume uses cubic units.
2. If the student is doing a reasonableness check, they must notice that the numerical work is fine but the unit makes the answer incomplete/incorrect.

So the correct final answer is 628 cm^3.

Marking

• 1 mark: identifies incorrect unit and states cm^3
• 1 mark: gives correct final answer 628 cm^3 with explanation

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Answer Key Snapshot

1. 120 cm^3
2. 12 m^3; student used area units instead of cubic units
3. 502.4 cm^3
4. 339.12 cm^3 is correct
5. 30 000 cm^3; 300 000 cm^3 is not reasonable
6. 3 cm
7. Yes; 615.44 cm^3 is reasonable
8. 0.12 m^3; yes, it is reasonable
9. Cylinder, 113.04 cm^3 vs prism 108 cm^3
10. Correct answer: 628 cm^3; the unit cm^2 is wrong

Mastery Interpretation

• 18-20 marks: strong mastery; learner is ready to move on while keeping unit checks as a habit.
• 16-17 marks: secure mastery; minor slips only.
• 12-15 marks: partial mastery; review unit-writing discipline and reasonableness checks.
• 0-11 marks: reteach before advancing.

Common Error Patterns to Diagnose from This Quiz

• Writing cm or cm^2 instead of cm^3
• Forgetting to square the radius in cylinder volume
• Trusting a calculator result without checking whether the unit makes sense
• Assuming decimal volumes are automatically unreasonable
• Missing simple size checks such as whether a result is ten times too large

Recommended Next Step

If the learner is below mastery, return first to the linked lesson, then assign targeted questions from the linked practice set before retrying this quiz or the broader unit mastery quiz.