Grade 8 Cylinder Volume Formulas: Unit Mastery Quiz

Use this record as a unit mastery check for the Grade 8 topic Cylinder Volume Formulas. For concept teaching, worked introduction, and additional practice, see the linked unit overview and practice set rather than treating this quiz as first instruction.

Linked records

• Overview and instruction: rea.m08.geometry-measurement.volume.basic-formulas.cylinders.overview
• Additional practice: rea.m08.geometry-measurement.volume.cylinder-volume-formulas.practice-set
• Related broader unit quiz: rea.m08.geometry-measurement.volume.basic-formulas.unit-mastery-quiz
• Related derivation-focused quiz: rea.m08.geometry-measurement.volume.cylinder-volume-derivation-quiz

Quiz directions

• Unless a question says otherwise, use the cylinder formula V = pi r^2 h.
• Give exact answers in terms of pi when possible.
• If an approximate answer is requested, round to the nearest tenth.
• Include units, and use cubic units for volume.

Recommended scoring

• 10 questions
• 20 marks total
• Most questions are worth 2 marks: 1 mark for correct setup and 1 mark for correct computation, units, or interpretation.

Questions

1. Basic volume from radius and height

A cylinder has radius 4 cm and height 9 cm. Find its volume.

[2 marks]

2. Volume from diameter and height

A cylinder has diameter 12 m and height 5 m. Find its volume.

[2 marks]

3. Decimal measurements

A can is shaped like a cylinder with radius 3.5 cm and height 8 cm. Find the volume to the nearest tenth of a cubic centimetre.

[2 marks]

4. Choose the correct measurement

A student writes V = pi(10)^2(7) for a cylinder labeled diameter 10 cm and height 7 cm. Is the student correct? If not, identify the error and find the correct volume.

[2 marks]

5. Solve for height

A cylinder has volume 200pi cm^3 and radius 5 cm. Find the height.

[2 marks]

6. Solve for radius

A cylinder has volume 432pi mm^3 and height 12 mm. Find the radius.

[2 marks]

7. Compare two cylinders

Cylinder A has radius 3 cm and height 10 cm. Cylinder B has radius 5 cm and height 4 cm. Which cylinder has the greater volume? Show enough work to justify your answer.

[2 marks]

8. Real-world capacity

A cylindrical water bottle has radius 3 cm and height 20 cm.

1. Find its volume in cm^3 in terms of pi.
2. Find its approximate volume to the nearest whole cubic centimetre.

[2 marks]

9. Reverse problem with diameter

A cylinder has volume 154pi cm^3 and height 14 cm. Find the diameter.

[2 marks]

10. Multi-step application

A cylindrical container has diameter 16 cm and height 15 cm. It is filled to 3/4 of its capacity. How much liquid is in the container? Give the exact answer in terms of pi, then an approximate answer to the nearest tenth.

[2 marks]

Full marking solutions

1. Basic volume from radius and height

V = pi r^2 h

Substitute r = 4 and h = 9:

V = pi(4)^2(9)
V = pi(16)(9)
V = 144pi

Answer: 144pi cm^3

Marking:

• 1 mark for correct substitution into V = pi r^2 h
• 1 mark for correct final answer with units

2. Volume from diameter and height

Diameter is 12 m, so radius is 6 m.

V = pi r^2 h
V = pi(6)^2(5)
V = pi(36)(5)
V = 180pi

Answer: 180pi m^3

Marking:

• 1 mark for converting diameter to radius correctly
• 1 mark for correct volume with units

3. Decimal measurements

V = pi r^2 h
V = pi(3.5)^2(8)
V = pi(12.25)(8)
V = 98pi

Approximate:

98pi ≈ 307.9

Answer: 98pi cm^3 ≈ 307.9 cm^3

Marking:

• 1 mark for correct setup
• 1 mark for correct approximation and units

4. Choose the correct measurement

The student is not correct.

Error: The student used the diameter as if it were the radius. If the diameter is 10 cm, then the radius is 5 cm.

Correct calculation:

V = pi r^2 h
V = pi(5)^2(7)
V = pi(25)(7)
V = 175pi

Answer: The error is using diameter instead of radius. The correct volume is 175pi cm^3.

Marking:

• 1 mark for identifying the radius/diameter error
• 1 mark for correct corrected volume

5. Solve for height

Given V = 200pi cm^3 and r = 5 cm.

Start with:

V = pi r^2 h

Substitute known values:

200pi = pi(5)^2 h
200pi = 25pi h

Divide both sides by 25pi:

h = 8

Answer: 8 cm

Marking:

• 1 mark for correct equation and substitution
• 1 mark for solving correctly

6. Solve for radius

Given V = 432pi mm^3 and h = 12 mm.

432pi = pi r^2(12)
432pi = 12pi r^2

Divide by 12pi:

r^2 = 36

So:

r = 6

Answer: 6 mm

Marking:

• 1 mark for correct setup and isolation of r^2
• 1 mark for correct radius

7. Compare two cylinders

Cylinder A:

V = pi(3)^2(10) = pi(9)(10) = 90pi cm^3

Cylinder B:

V = pi(5)^2(4) = pi(25)(4) = 100pi cm^3

Since 100pi > 90pi, Cylinder B has greater volume.

Answer: Cylinder B has the greater volume.

Marking:

• 1 mark for one correct volume
• 1 mark for the second correct volume and correct comparison

8. Real-world capacity

1. Exact volume:

V = pi(3)^2(20)
V = pi(9)(20)
V = 180pi cm^3

2. Approximate volume:

180pi ≈ 565.5

To the nearest whole number:

566 cm^3

Answer: 180pi cm^3, approximately 566 cm^3

Marking:

• 1 mark for correct exact volume
• 1 mark for correct approximation

9. Reverse problem with diameter

Given V = 154pi cm^3 and h = 14 cm.

154pi = pi r^2(14)
154pi = 14pi r^2

Divide by 14pi:

r^2 = 11

So:

r = sqrt(11) cm

Diameter is twice the radius:

d = 2sqrt(11) cm

Approximate value:

d ≈ 6.6 cm

Answer: 2sqrt(11) cm (about 6.6 cm)

Marking:

• 1 mark for solving correctly for radius
• 1 mark for converting radius to diameter

10. Multi-step application

Diameter is 16 cm, so radius is 8 cm.

First find full capacity:

V = pi r^2 h
V = pi(8)^2(15)
V = pi(64)(15)
V = 960pi cm^3

Now find 3/4 of the capacity:

(3/4)(960pi) = 720pi cm^3

Approximate:

720pi ≈ 2261.9

Answer: 720pi cm^3 ≈ 2261.9 cm^3

Marking:

• 1 mark for correct full cylinder volume
• 1 mark for correctly finding 3/4 of the volume and giving units

Answer key only

1. 144pi cm^3
2. 180pi m^3
3. 98pi cm^3 ≈ 307.9 cm^3
4. No; diameter was used as radius. Correct volume: 175pi cm^3
5. 8 cm
6. 6 mm
7. Cylinder B
8. 180pi cm^3 ≈ 566 cm^3
9. 2sqrt(11) cm ≈ 6.6 cm
10. 720pi cm^3 ≈ 2261.9 cm^3

Mastery threshold recommendation

For a Grade 8 self-taught learner, a strong mastery threshold is:

• 16/20 or better, with
• no major formula-selection error, and
• no repeated confusion between radius and diameter, and
• units correct on at least 8 of 10 questions.

Interpreting results

• 18-20: Secure mastery. The learner is ready to move to mixed volume-formula selection and richer applications.
• 16-17: Meets mastery. A short review of any missed reverse or unit questions is still worthwhile.
• 13-15: Developing but not yet secure. Revisit the overview and complete additional targeted practice.
• 12 or below: Re-teach before advancing, especially base-area reasoning, radius-versus-diameter conversion, and solving for missing dimensions.

Common error patterns to diagnose from this quiz

• Using diameter directly in r^2.
• Forgetting to square the radius.
• Writing square units instead of cubic units.
• Dropping pi in exact-answer questions.
• Solving for radius correctly but forgetting to double it when the question asks for diameter.
• Computing the full cylinder volume correctly in an application question but not adjusting for a fraction such as 3/4 full.

Suggested next step after the quiz

• If the learner missed mostly computation or unit details, assign selected questions from rea.m08.geometry-measurement.volume.cylinder-volume-formulas.practice-set.
• If the learner can compute but cannot explain why the formula works, use rea.m08.geometry-measurement.volume.cylinder-volume-derivation-quiz next.