Virginia SOL 8.MG.2.b
The Standard
Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.
Virginia Standards of Learning for Mathematics · The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the volume of cones and square-based pyramids from objects and labeled diagrams. They use V = 1/3πr²h or V = 1/3s²h and report cubic units.
What Mastery Looks Like
- Students choose the correct formula and identify the needed dimensions from a model or diagram. They calculate accurately, include cubic units, and explain why each volume is one-third of a related prism or cylinder.
Common Misconceptions
- Students often forget the one-third factor or use slant height instead of perpendicular height. They may confuse radius with diameter or fail to square the pyramid’s base side length.
How to Assess It
- Give students one labeled cone and one labeled square-based pyramid. Ask them to write each formula, substitute the dimensions, and calculate both volumes with cubic units.
Lesson moves
Ways to Teach It
Fill a cone and square-based pyramid with rice, then pour each into a matching cylinder or prism three times.
Ask students to explain in writing why perpendicular height, rather than slant height, belongs in each volume formula.
Play a formula sort with cards showing solids, dimensions, formulas, substitutions, and answers for students to match.
Compare the capacities of a conical paper cup and a square-based pyramid package using measured dimensions.
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Printable 8.MG.2.b Worksheet
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Related Standards
- 8.MG.2
The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids.
- 8.MG.2.d
Solve problems in context involving volume of cones and square-based pyramids and the surface area of square-based pyramids.
- 8.MG.2.c
Examine and explain the relationship between the volume of cones and cylinders, and the volume of rectangular prisms and square based pyramids.
- 8.MG.2.a
Determine the surface area of square-based pyramids by using concrete objects, nets, diagrams, and formulas.
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