Virginia SOL 8.MG.2.d
The Standard
Solve problems in context involving volume of cones and square-based pyramids and the surface area of square-based pyramids.
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 identify needed dimensions from diagrams and word problems. They calculate cone and square pyramid volumes and square pyramid surface area, then report answers with correct units.
What Mastery Looks Like
- Students select the correct formula and substitute the correct measurements. They accurately find cone and pyramid volumes and pyramid surface area, use proper units, and explain answers in context.
Common Misconceptions
- Students may use diameter instead of radius or confuse slant height with perpendicular height. They may omit the pyramid’s base from surface area or label volume with square units.
How to Assess It
- Exit ticket: A cone has radius 3 cm and height 8 cm. Find its volume in terms of π, then explain which height the formula requires.
Lesson moves
Ways to Teach It
Give pairs a cardstock pyramid net to measure, assemble, and use to calculate total surface area.
Ask students to explain why slant height finds pyramid surface area but perpendicular height finds pyramid volume.
Run a card sort matching cone and pyramid diagrams, formulas, measurements, units, and completed solutions.
Compare cone-shaped cups and square pyramid packages, then calculate how much each holds or how much material covers it.
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Printable 8.MG.2.d Worksheet
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Related Standards
- 8.MG.2.b
Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.
- 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.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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