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Mathematics · Grade 10

Area, Surface Area and Volume

Learners justify area formulas by cutting and rearranging, including an informal limit argument for the area of a circle, and explain volume formulas with Cavalieri's principle and the one-third relationship between pyramids and prisms. They compute surface areas from nets, identify cross-sections and solids of revolution, and apply density and scale factors in modeling problems. An optional honors lesson shows three pyramids filling a cube.

  • 5 lessons
  • About 135 minutes
  • Area, surface area and volume check: 11 questions
  • Ways to answer: choose an answer, match pairs, type a number, sort into groups and write a short answer
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What learners will discover

  • Justify and apply area formulas for parallelograms, triangles, trapezoids, regular polygons and circles using dissection and an informal limit argument.
  • Apply volume formulas for prisms, cylinders, pyramids, cones and spheres, and explain them using Cavalieri's principle and the one-third relationship.
  • Compute surface areas of prisms, cylinders, pyramids, cones and spheres, and identify cross-sections of solids and solids of revolution.
  • Model situations with density (per unit area or volume) and with the effects of scale factors on area and volume.

Lessons

  1. Area formulas and why they work 6 steps3 practiceabout 30 min
  2. Volume and Cavalieri's principle 6 steps4 practiceabout 32 min
  3. Surface area, cross-sections and solids of revolution 6 steps4 practiceabout 30 min
  4. Density and scale in modeling 6 steps4 practiceabout 28 min
  5. Going further (honors): three pyramids make a cube 3 steps1 practiceabout 15 min
  6. Area, surface area and volume check 11 questions at the end

Keep exploring

More 10th grade math

Guide for grown-ups