Grade 8 Surface Area: Base Perimeter and Surface Area Unit Mastery Quiz

Use of this record

This record is an end-of-unit assessment, not the main teaching sequence. For concept development, nets, and broader surface-area instruction, use rea.m08.geometry-measurement.surface-area.overview. For decimal computation support, use rea.m08.number.decimals-and-percents.decimal-operations.unit-mastery-quiz if arithmetic errors interfere with geometry performance.

Quiz focus

This quiz checks whether you can:

• identify the base and its perimeter
• use lateral area = P_base x height for right prisms
• connect cylinder curved surface area to circumference x height
• find total surface area with SA = 2B + Ph for prisms and SA = 2pi r^2 + 2pi rh for cylinders
• solve reverse problems with a missing dimension
• track linear units versus square units correctly

Quiz directions

• Show all work.
• Use pi ≈ 3.14 unless the question says otherwise.
• Answers for surface area must be in square units.
• Total: 30 marks.

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Questions

1. Rectangular prism from base-perimeter method (2 marks)

A right rectangular prism has base length 8 cm, base width 5 cm, and height 12 cm.

Find:

1. the perimeter of the base
2. the lateral surface area

2. Total surface area of a triangular prism (3 marks)

A right triangular prism has a triangular base with side lengths 6 m, 8 m, and 10 m. The triangle's area is 24 m^2. The prism length is 15 m.

Find the total surface area.

3. Explain the formula connection (2 marks)

A student says, "For any right prism, the lateral area is P_base x height."

Explain why this makes sense using the idea of faces or a net.

4. Cylinder curved surface area (3 marks)

A cylinder has radius 4 cm and height 9 cm.

Find:

1. the circumference of the base
2. the curved surface area
3. the total surface area

Use pi ≈ 3.14.

5. Error analysis (3 marks)

A student is finding the total surface area of a cylinder with radius 3 cm and height 10 cm. They write:

SA = 2pi r + 2pi rh = 2(3.14)(3) + 2(3.14)(3)(10) = 18.84 + 188.4 = 207.24 cm^2

Identify the mistake and find the correct total surface area.

6. Missing prism height (3 marks)

A right prism has base area 18 cm^2, base perimeter 20 cm, and total surface area 156 cm^2.

Find the prism height.

7. Polygon prism application (4 marks)

A regular pentagonal prism has:

• base perimeter 35 cm
• base area 84 cm^2
• height 11 cm

Find:

1. the lateral surface area
2. the total surface area
3. the fraction of the total surface area that is lateral area

8. Reverse cylinder problem (4 marks)

A closed cylinder has total surface area 301.44 cm^2 and radius 4 cm. Use pi = 3.14.

Find the height.

9. Compare two solids (3 marks)

Solid A is a right rectangular prism with base 7 cm by 3 cm and height 10 cm. Solid B is a cylinder with radius 3 cm and height 10 cm.

Which solid has the greater lateral surface area? Show the calculation for each and state by how much. Use pi ≈ 3.14.

10. Packaging context (3 marks)

A label wraps exactly once around the curved side of a can, covering the full height but not the top or bottom. The can has diameter 8 cm and height 13 cm.

Find:

1. the area of the label
2. the total surface area of the whole can

Use pi ≈ 3.14.

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Full marking solutions

1. Rectangular prism from base-perimeter method

Base perimeter: P_base = 2(8 + 5) = 26 cm

Lateral surface area: LA = P_base x h = 26 x 12 = 312 cm^2

Answer:

• base perimeter = 26 cm
• lateral surface area = 312 cm^2

Marking:

• 1 mark for correct base perimeter
• 1 mark for correct lateral area with square units

2. Total surface area of a triangular prism

For a right prism, SA = 2B + Ph

Here:

• B = 24 m^2
• P = 6 + 8 + 10 = 24 m
• h = 15 m

Lateral area: Ph = 24 x 15 = 360 m^2

Total surface area: SA = 2(24) + 360 = 48 + 360 = 408 m^2

Answer: 408 m^2

Marking:

• 1 mark for finding base perimeter
• 1 mark for correct lateral area
• 1 mark for correct total surface area

3. Explain the formula connection

When you unfold a right prism into a net, the side faces line up into a strip of rectangles. The width of that strip is the distance all the way around the base, which is the base perimeter. The height of every side face is the prism height. So the total side area is a rectangle with area P_base x height.

Answer: The lateral area equals P_base x height because the side faces together form a rectangle whose width is the base perimeter and whose height is the prism height.

Marking:

• 1 mark for referring to the net or side faces forming a strip/rectangle
• 1 mark for correctly identifying width as base perimeter and height as prism height

4. Cylinder curved surface area

Circumference: C = 2pi r = 2(3.14)(4) = 25.12 cm

Curved surface area: CSA = Ch = 25.12 x 9 = 226.08 cm^2

Area of two circular bases: 2pi r^2 = 2(3.14)(4^2) = 2(3.14)(16) = 100.48 cm^2

Total surface area: SA = 226.08 + 100.48 = 326.56 cm^2

Answer:

• circumference = 25.12 cm
• curved surface area = 226.08 cm^2
• total surface area = 326.56 cm^2

Marking:

• 1 mark for correct circumference
• 1 mark for correct curved surface area
• 1 mark for correct total surface area

5. Error analysis

The mistake is in the first term. The student used 2pi r, which is circumference, not the area of the two circular bases. The correct term is 2pi r^2.

Correct calculation: SA = 2pi r^2 + 2pi rh = 2(3.14)(3^2) + 2(3.14)(3)(10) = 2(3.14)(9) + 188.4 = 56.52 + 188.4 = 244.92 cm^2

Answer: The student used circumference instead of the area of two circles. Correct total surface area: 244.92 cm^2.

Marking:

• 1 mark for identifying that 2pi r should be 2pi r^2
• 1 mark for correct substitution
• 1 mark for correct final answer

6. Missing prism height

Use SA = 2B + Ph.

Substitute known values: 156 = 2(18) + 20h 156 = 36 + 20h 120 = 20h h = 6

Answer: 6 cm

Marking:

• 1 mark for correct equation
• 1 mark for correct rearrangement
• 1 mark for correct height

7. Polygon prism application

Lateral surface area: LA = Ph = 35 x 11 = 385 cm^2

Total surface area: SA = 2B + Ph = 2(84) + 385 = 168 + 385 = 553 cm^2

Fraction that is lateral area: LA / SA = 385 / 553

This fraction does not simplify because 553 = 7 x 79 and 385 = 5 x 7 x 11, so there is no common factor after cancelling none.

As a decimal: 385 / 553 ≈ 0.696 So about 69.6% of the surface area is lateral.

Answer:

• lateral surface area = 385 cm^2
• total surface area = 553 cm^2
• fraction lateral = 385/553 (about 69.6%)

Marking:

• 1 mark for correct lateral area
• 1 mark for correct total surface area
• 2 marks for correct fraction or percent, with work

8. Reverse cylinder problem

Use: SA = 2pi r^2 + 2pi rh

Substitute known values: 301.44 = 2(3.14)(4^2) + 2(3.14)(4)h 301.44 = 2(3.14)(16) + 25.12h 301.44 = 100.48 + 25.12h 200.96 = 25.12h h = 8

Answer: 8 cm

Marking:

• 1 mark for correct equation and substitution
• 1 mark for isolating the lateral term
• 1 mark for correct division
• 1 mark for correct final height

9. Compare two solids

Solid A: rectangular prism Base perimeter: P = 2(7 + 3) = 20 cm

Lateral area: LA = Ph = 20 x 10 = 200 cm^2

Solid B: cylinder Circumference: C = 2pi r = 2(3.14)(3) = 18.84 cm

Curved surface area: CSA = Ch = 18.84 x 10 = 188.4 cm^2

Compare: 200 - 188.4 = 11.6 cm^2

Answer: Solid A has the greater lateral surface area by 11.6 cm^2.

Marking:

• 1 mark for prism lateral area
• 1 mark for cylinder lateral area
• 1 mark for correct comparison with difference

10. Packaging context

Diameter 8 cm gives radius r = 4 cm.

Label area is the curved surface area only: CSA = 2pi rh = 2(3.14)(4)(13) = 25.12 x 13 = 326.56 cm^2

Area of top and bottom: 2pi r^2 = 2(3.14)(16) = 100.48 cm^2

Total surface area: SA = 326.56 + 100.48 = 427.04 cm^2

Answer:

• label area = 326.56 cm^2
• total surface area = 427.04 cm^2

Marking:

• 1 mark for using radius correctly
• 1 mark for correct label area
• 1 mark for correct total surface area

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Mastery threshold recommendation

Recommended mastery threshold: 24/30 or better, with evidence that the learner can correctly do both of the following without major prompting:

• use LA = P_base x height or CSA = circumference x height
• distinguish lateral area from total surface area

Suggested interpretation

• 27-30: secure mastery; ready for mixed surface-area applications
• 24-26: meets mastery; minor review only
• 18-23: developing; revisit base perimeter, nets, and square-unit reasoning
• below 18: reteach from rea.m08.geometry-measurement.surface-area.overview before reassessment

Common error patterns to watch for

• Using linear units instead of square units for area
• Forgetting to include both bases in total surface area
• Using 2pi r where pi r^2 is required
• Mixing up prism height with a base edge length
• Adding face areas inconsistently instead of organizing with 2B + Ph

Record linkage

• Use rea.m08.geometry-measurement.surface-area.overview for the teaching sequence, nets, and conceptual build-up behind these questions.
• Use rea.m08.number.decimals-and-percents.decimal-operations.unit-mastery-quiz if numerical errors, rather than geometry errors, are blocking success.
• Compare the assessment style with rea.m08.geometry-measurement.volume.basic-formulas.unit-mastery-quiz for parallel expectations in the adjacent measurement strand.