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Volume of Irregular Solids

Name of Corresponding Unit Plan: Archaeological Documentation

Grade Level: 5-12

Common Core Standards:
RS9-10. 3. Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

Content Areas: Math, Science

Recommended Length/Duration: 45-60 minute period

Learning Goals: Students will learn to measure and calculate the volumes of various liquids irregular solids.

Description/Sequence:

  1. Before class gather a collection of several small, irregularly shaped objects.
  2. Discuss the definition of volume.  Point out that many objects have regular shapes and that their volume can be calculated by measuring their dimensions and using standard formulas.  Other objects can be subdivided into two or more regular shapes that can be measured and then added together.  However, most things do not have regular shapes and cannot be easily measured or have their volumes determined through calculations.
  3. Hold up an irregular shaped object and ask how we can find the volume of such a shape.  Accept various responses.  Ask students to explain how their approach would work.  Ask others if they agree or disagree.  Eventually the discussion should lead to a description of volume measurement by displacement.
  4. Describe how an object placed in water will displace the water.  In a container, this will cause the water to rise.  Demonstrate with a large graduated cylinder how the water rises as an object displaces it.  If the object is fully submerged, it will displace its full volume.
  5. Point out that volume of the water displaced equals the volume of the object.
  6. Organize students into small work groups.  Each group will need a graduated cylinder or measuring cup with a measured amount of water.  Have them submerge each object in the sample collection to determine its volume.  Have them record their results on their worksheet.
  7. When students have measured all of the samples, compare results.  Clarify and errors or questions.

Assessments: Check worksheets for accuracy.

Materials/Resources: Volume of Irregular Solids Worksheets (pdf), Graduated Cylinders or Measuring Cups, Collection of various irregular solids.

Special Considerations: Weaker students could be partnered with stronger students.

Scientific measurements are generally easier to take and calculate in metric than in English units.  Additional work may be needed if students are not familiar with metric measurements, or if the teacher chooses to use English units.

Extensions:
Additional measurements and calculations of volume can be taken at home. 

Students may want to research the origin of Archimedes Principle.

Students might want to try and find the volume of their own body.