Grade 8 Prism Volume as Base Area Times Height: Unit Mastery Quiz with Full Solutions

Position in the unit

This record is a focused mastery check for the topic Prism Volume as Base Area Times Height in Grade 8 geometry and measurement.

Use these linked records for teaching and practice before this quiz:

• rea.m08.geometry-measurement.volume.basic-formulas.prism-bh.practice-set for graduated skill-building on V = Bh
• rea.m08.geometry-measurement.volume.basic-formulas.unit-mastery-quiz for a broader mixed assessment across volume formulas

This quiz does not restate the full lesson. It checks whether the learner can now use the prism structure reliably.

Unit mastery focus

A learner is ready to master this topic if they can:

• identify the base area B
• identify the perpendicular height h
• use V = Bh correctly
• solve for a missing value when two of V, B, and h are known
• keep square units for area and cubic units for volume
• ignore non-perpendicular lengths that are not the prism height

Quiz instructions

• Show all work.
• Use the formula V = Bh when appropriate.
• Include units in every final answer.
• Total: 20 marks

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Questions

1. Direct substitution with a rectangular base (2 marks)

A prism has base area 18 cm^2 and perpendicular height 7 cm. Find its volume.

2. Triangular prism (2 marks)

The base of a prism is a triangle with base 8 m and triangle height 5 m. The prism height is 12 m. Find the prism's volume.

3. Trapezoidal prism (2 marks)

The base of a prism is a trapezoid with parallel sides 6 cm and 10 cm, and trapezoid height 4 cm. The prism height is 9 cm. Find the volume.

4. Reverse problem: find prism height (2 marks)

A prism has volume 180 cm^3 and base area 15 cm^2. Find the perpendicular height.

5. Reverse problem: find base area (2 marks)

A prism has volume 264 m^3 and perpendicular height 11 m. Find the base area.

6. Choosing the correct height (2 marks)

A prism has a base area of 24 cm^2. A slanted edge on the side measures 10 cm, but the perpendicular distance between the bases is 8 cm. Find the volume.

7. Composite base (2 marks)

The base of a prism is an L-shape made from a 9 cm by 7 cm rectangle with a 3 cm by 2 cm corner removed. The prism height is 5 cm. Find the volume.

8. Unit conversion in context (2 marks)

A prism has base area 0.6 m^2 and height 250 cm. Find the volume in m^3.

9. Application problem (2 marks)

A storage trough is shaped like a prism. Its cross-sectional base area is 1.8 m^2, and its length is 3.5 m. Find its volume. Then state its capacity in litres. Use 1 m^3 = 1000 L.

10. Reasoning about the formula (2 marks)

A student says, "To find any prism volume, multiply the area of a face by any edge length." Is the student correct? Explain what must be multiplied, and why.

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Full marking key and solutions

1. Direct substitution with a rectangular base (2 marks)

V = Bh

V = 18 x 7

V = 126

Answer: 126 cm^3

Marking:

• 1 mark for correct use of V = Bh
• 1 mark for correct answer with units

2. Triangular prism (2 marks)

First find the triangular base area:

B = (1/2) x 8 x 5 = 20 m^2

Now use V = Bh:

V = 20 x 12 = 240

Answer: 240 m^3

Marking:

• 1 mark for correct base area
• 1 mark for correct volume with units

3. Trapezoidal prism (2 marks)

Base area of trapezoid:

B = (1/2)(6 + 10) x 4

B = (1/2)(16) x 4

B = 8 x 4 = 32 cm^2

Now volume:

V = Bh = 32 x 9 = 288

Answer: 288 cm^3

Marking:

• 1 mark for correct trapezoid area
• 1 mark for correct volume with units

4. Reverse problem: find prism height (2 marks)

V = Bh

180 = 15h

h = 180 / 15 = 12

Answer: 12 cm

Marking:

• 1 mark for rearranging or equivalent division step
• 1 mark for correct answer with units

5. Reverse problem: find base area (2 marks)

V = Bh

264 = B x 11

B = 264 / 11 = 24

Answer: 24 m^2

Marking:

• 1 mark for correct setup
• 1 mark for correct answer with square units

6. Choosing the correct height (2 marks)

For prism volume, use the perpendicular height, not the slanted edge.

So:

V = Bh = 24 x 8 = 192

Answer: 192 cm^3

Marking:

• 1 mark for selecting 8 cm as the correct height
• 1 mark for correct volume with units

7. Composite base (2 marks)

Find the L-shaped base area:

B = 9 x 7 - 3 x 2

B = 63 - 6 = 57 cm^2

Now volume:

V = Bh = 57 x 5 = 285

Answer: 285 cm^3

Marking:

• 1 mark for correct composite base area
• 1 mark for correct volume with units

8. Unit conversion in context (2 marks)

Convert height first:

250 cm = 2.5 m

Now use V = Bh:

V = 0.6 x 2.5 = 1.5

Answer: 1.5 m^3

Marking:

• 1 mark for correct unit conversion
• 1 mark for correct volume with units

9. Application problem (2 marks)

Volume:

V = Bh = 1.8 x 3.5 = 6.3 m^3

Convert to litres:

6.3 m^3 = 6300 L

Answer: 6.3 m^3 or 6300 L

Marking:

• 1 mark for correct volume in m^3
• 1 mark for correct conversion to litres

10. Reasoning about the formula (2 marks)

The student is not correct.

To find prism volume, you must multiply the area of one base by the perpendicular distance between the two congruent bases:

V = Bh

You cannot use just any face area or any edge length, because the formula depends on stacking equal base layers through the prism's perpendicular height.

Answer: The correct rule is to multiply base area by perpendicular height, not any face area by any edge.

Marking:

• 1 mark for saying the statement is incorrect
• 1 mark for explaining that the correct quantities are base area and perpendicular height

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Mastery threshold recommendation

Recommended mastery threshold: 16/20 (80%), with no major conceptual error on Questions 4, 5, 6, or 10.

Interpretation:

• 18-20: secure mastery
• 16-17: adequate mastery, ready to move on
• 13-15: partial mastery; review reverse problems and height selection
• 0-12: reteach the structure V = Bh and practise identifying B and perpendicular h

Diagnostic reading of errors

Common error patterns and what they mean:

• Using a slanted edge instead of perpendicular height: the learner does not yet understand what h means in V = Bh.
• Writing area units instead of volume units: the learner is not distinguishing cm^2 from cm^3.
• Failing reverse problems: the learner may know the formula forward but not the relationship among V, B, and h.
• Multiplying base dimensions and prism height without first finding a non-rectangular base area: the learner needs more work on seeing B as a single quantity.

Short remediation guidance

If the learner is below mastery:

• revisit the linked prism-specific practice set first
• then reattempt Questions 4, 5, 6, and 10
• finally use the broader linked volume unit quiz to check transfer across prism and cylinder contexts