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MathidiaMathematics Academy
Advanced geometry and solids
Lesson 54 of 75
Challenge

Density in compound solids

Objective. Combine volume, mass and unit conversion accurately.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Density in compound solids is developed here as connected GCSE mathematics, not a memorised shortcut. Connect similarity, trigonometry and compound measures in space. The lesson moves from a precise representation and key definitions to fluent procedure, linked reasoning and an unfamiliar application. Learners compare possible methods, state restrictions and assumptions, preserve exact values where appropriate, and justify accuracy, notation and units before evaluating whether the result is mathematically and contextually reasonable.

Worked example

Match criterion to information.

right angle, hypotenuse, …
Illustrated card showing right angle, hypotenuse, side | two sides, included angle | two angles, side
  1. 1Translate the information into a labelled diagram, table, graph or algebraic statement and identify every constraint.
  2. 2Select the most efficient GCSE method, explain why its conditions apply, and keep exact values until approximation is requested.
  3. 3Carry out each transformation on a separate justified line, tracking signs, units, domains and required accuracy.
  4. 4Verify with substitution, an inverse method, estimation or a second representation. The checked result is right angle, hypotenuse, side | two sides, included angle | two angles, side.

Answer: right angle, hypotenuse, side | two sides, included angle | two angles, side

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. A common error in density in compound solids is applying a familiar rule before checking its conditions, domain or direction. Name the structure first, retain exact values, and test the final result against every original constraint.

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