Grade 8 Unit Mastery Quiz: Selecting and Using the Correct Volume Formula

This quiz focuses on one skill: choosing the correct volume formula before calculating. It assumes prior study of the lesson on formula selection and the broader unit on basic volume formulas.

Linked records for teaching and review:

• rea.m08.geometry-measurement.volume.basic-formulas.formula-selection.lesson for instruction, worked examples, and misconception repair
• rea.m08.geometry-measurement.volume.basic-formulas.unit-mastery-quiz for a broader end-of-unit assessment across prism and cylinder volume skills
• rea.m08.geometry-measurement.volume.cylinder-volume-derivation-quiz for deeper understanding of why V = pi r^2 h works

Use this record as an assessment, not as first instruction.

Formula Reminder

• Right rectangular prism: V = lwh
• Cylinder: V = pi r^2 h

Marking Structure

• 10 questions
• 20 marks total
• Suggested value: 2 marks each
• Full marks require both correct formula selection and correct calculation/setup

Quiz Questions

1. Identify the correct formula

A solid has length 9 cm, width 4 cm, and height 7 cm.

1. Name the solid.
2. Write the correct volume formula.

2. Identify the correct formula from radius information

A can is shaped like a cylinder. Its radius is 5 cm and its height is 12 cm.

1. Name the solid.
2. Write the correct volume formula.

3. Compute volume of a rectangular prism

A box has dimensions 11 cm by 3 cm by 8 cm. Find its volume.

4. Compute volume of a cylinder

A cylinder has radius 4 m and height 10 m. Find its volume in exact form and as a decimal rounded to the nearest tenth.

5. Choose between diameter and radius

A cylindrical water container has diameter 14 cm and height 9 cm. Find its volume.

6. Spot and correct the wrong formula choice

A student sees a cylinder with radius 3 cm and height 8 cm and writes: V = 3 x 8 = 24 cm^3 Explain what is wrong, then find the correct volume.

7. Missing dimension in a rectangular prism

A right rectangular prism has volume 180 cm^3, length 9 cm, and width 4 cm. Find the height.

8. Missing dimension in a cylinder

A cylinder has volume 245pi cm^3 and height 5 cm. Find the radius.

9. Mixed formula selection in context

A cereal box is a rectangular prism with dimensions 30 cm x 20 cm x 6 cm. A juice can is a cylinder with radius 3 cm and height 12 cm.

1. Find the volume of each object.
2. Which object has the greater volume?

10. Multi-step mastery problem

A storage bin is a rectangular prism with volume 960 cm^3. Its length is 12 cm and its width is 10 cm. A paint can is a cylinder with the same height as the bin's missing dimension and radius 4 cm.

1. Find the missing height of the bin.
2. Find the volume of the cylinder.
3. Which formula was needed for each solid, and why?

Full Solutions and Marking Key

1. Identify the correct formula

The measurements are length, width, and height, so the solid is a right rectangular prism.

Correct formula: V = lwh

Marking:

• 1 mark for identifying right rectangular prism
• 1 mark for V = lwh

2. Identify the correct formula from radius information

A can is shaped like a cylinder. The measurement given is radius, which is used for circular bases.

Correct formula: V = pi r^2 h

Marking:

• 1 mark for identifying cylinder
• 1 mark for V = pi r^2 h

3. Compute volume of a rectangular prism

Use V = lwh

V = 11 x 3 x 8 V = 33 x 8 V = 264

Volume = 264 cm^3

Marking:

• 1 mark for correct formula/setup
• 1 mark for 264 cm^3

4. Compute volume of a cylinder

Use V = pi r^2 h

V = pi(4)^2(10) V = pi(16)(10) V = 160pi

Exact volume = 160pi m^3

Decimal approximation: 160pi approx 502.7

Volume approx 502.7 m^3

Marking:

• 1 mark for correct substitution
• 1 mark for 160pi m^3 and 502.7 m^3 (nearest tenth)

5. Choose between diameter and radius

The solid is a cylinder, but the formula uses radius, not diameter.

Diameter = 14 cm, so radius = 7 cm

Use V = pi r^2 h

V = pi(7)^2(9) V = pi(49)(9) V = 441pi

Volume = 441pi cm^3 Approximate volume: 441pi approx 1385.4

Volume approx 1385.4 cm^3

Marking:

• 1 mark for converting diameter to radius
• 1 mark for correct volume

6. Spot and correct the wrong formula choice

The student multiplied only radius and height. That does not match the cylinder formula. A cylinder needs the area of its circular base first, so the correct formula is V = pi r^2 h.

Now calculate: V = pi(3)^2(8) V = pi(9)(8) V = 72pi

Volume = 72pi cm^3 Approximate volume: 72pi approx 226.2

Volume approx 226.2 cm^3

Marking:

• 1 mark for explaining that the wrong formula was used and the base area was missing
• 1 mark for correct volume

7. Missing dimension in a rectangular prism

Use V = lwh

180 = 9 x 4 x h 180 = 36h h = 180 / 36 h = 5

Height = 5 cm

Marking:

• 1 mark for correct equation
• 1 mark for 5 cm

8. Missing dimension in a cylinder

Use V = pi r^2 h

245pi = pi r^2 (5) Divide both sides by pi: 245 = 5r^2 r^2 = 49 r = 7

Radius = 7 cm

Marking:

• 1 mark for correct equation and simplification
• 1 mark for 7 cm

9. Mixed formula selection in context

For the cereal box, use the rectangular prism formula: V = lwh

V = 30 x 20 x 6 V = 600 x 6 V = 3600

Cereal box volume = 3600 cm^3

For the juice can, use the cylinder formula: V = pi r^2 h

V = pi(3)^2(12) V = pi(9)(12) V = 108pi 108pi approx 339.3

Juice can volume approx 339.3 cm^3

Compare: 3600 cm^3 > 339.3 cm^3

The cereal box has the greater volume.

Marking:

• 1 mark for both correct setups
• 1 mark for both volumes and correct comparison

10. Multi-step mastery problem

Part 1: Find the missing height of the bin

The bin is a rectangular prism, so use V = lwh.

960 = 12 x 10 x h 960 = 120h h = 960 / 120 h = 8

Missing height = 8 cm

Part 2: Find the volume of the cylinder

The cylinder has height 8 cm and radius 4 cm. Use V = pi r^2 h

V = pi(4)^2(8) V = pi(16)(8) V = 128pi

Volume = 128pi cm^3 Approximate volume: 128pi approx 402.1

Volume approx 402.1 cm^3

Part 3: Explain the formula choice

• The bin used V = lwh because it is a right rectangular prism with three linear dimensions: length, width, and height.
• The paint can used V = pi r^2 h because it is a cylinder with a circular base, so the base area is pi r^2.

Marking:

• 1 mark for finding the bin's height
• 1 mark for correct cylinder volume and explanation of formula choice

Mastery Threshold Recommendation

Recommended mastery threshold: 16/20 or better, with no major formula-selection error on more than one question.

Interpretation:

• 18-20: Secure mastery. The learner consistently selects the correct formula and handles substitutions accurately.
• 16-17: Meets mastery. Minor arithmetic or rounding slips may appear, but formula choice is mostly reliable.
• 13-15: Approaching mastery. The learner should review radius vs diameter, missing-dimension equations, and matching shape to formula.
• 12 or below: Not yet secure. Return to the lesson on formula selection before moving on.

Common Error Check

Use this short checklist while marking:

• Did the learner choose prism vs cylinder correctly?
• For cylinders, did the learner use radius rather than diameter?
• Did the learner square only the radius, not the whole expression incorrectly?
• Did the learner include cubic units?
• In reverse problems, did the learner solve for the unknown after writing the correct volume equation?

Suggested Follow-Up

• If errors are mostly about cylinders, review rea.m08.geometry-measurement.volume.cylinder-volume-derivation-quiz.
• If errors are mixed across prism and cylinder basics, review rea.m08.geometry-measurement.volume.basic-formulas.unit-mastery-quiz.
• If errors begin when setting up equations for missing dimensions, use rea.m08.algebra.solving-linear-equations.linear-modeling.variables.unit-mastery-quiz as support for equation setup and unknowns.