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Solve both parts and justify the conditions used. Part A: Similar solids have linear scale factor 3 from small to large. Find the surface-area ratio. Part B: In the 45° half-depth oblique convention, an original depth is d. Find its drawn length.

Read the idea, work independently, then explain what changed.

TOPIC 01

Introduction to solid geometry: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Solve both parts and justify the conditions used. Part A: Similar solids have linear scale factor 3 from small to large. Find the surface-area ratio. Part B: In the 45° half-depth oblique convention, an original depth is d. Find its drawn length.

B: d=18\begin{gathered}\text{B: }d=18\end{gathered}
  • Use the domain, units and sampling assumptions stated in the question.
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
A: Choose the correct surface or volume formula and keep units and similarity powers consistent.
Hint 2
B: Distinguish the actual spatial object from the stated oblique drawing convention.
Worked solution
  1. Part A reasoning

  2. Choose the correct surface or volume formula and keep units and similarity powers consistent.

  3. Calculate or simplify this relation.

    Slarge/Ssmall=32=9S_{\text{large}}/S_{\text{small}}=3^2=9
  4. The volume ratio would instead be 27.

  5. Part B reasoning

  6. Distinguish the actual spatial object from the stated oblique drawing convention.

  7. Calculate or simplify this relation.

    d′=18/2=9d'=18/2=9
  8. This is a drawing convention, not a change in the solid.

A: The requested value is 9. B: The requested value is 9.

Checks and common pitfalls: The volume ratio would instead be 27. This is a drawing convention, not a change in the solid.

Reasoning checklist · self / teacher assessment
  • Solve part A with its stated restrictions.
  • Solve part B using an appropriate representation.
  • Give the reasoning and check conditions in both parts.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗