8.6.B
The Standard
model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare a cylinder and cone with the same radius and height. They use a physical or visual model to show that three cone volumes equal one cylinder volume, then connect that result to the formulas.
What Mastery Looks Like
- Given matching dimensions, students calculate both volumes and explain why the cone holds one third as much as the cylinder. They use the formulas accurately and label answers with cubic units.
Common Misconceptions
- Students may think the cone holds half as much as the cylinder instead of one third. They may forget to multiply by one third, use diameter as radius, or write square units instead of cubic units. Some compare shapes whose radii or heights do not match.
How to Assess It
- Exit ticket: A cone and cylinder both have radius 3 cm and height 8 cm. Find both volumes and explain their numerical relationship in one sentence.
Lesson moves
Ways to Teach It
Use a matching plastic cone and cylinder, then pour rice from the cone three times to fill the cylinder.
Ask students to write why the factor one third belongs in the cone volume formula, using evidence from the rice model.
Run a card sort matching cylinder dimensions, cylinder volumes, cone volumes, and equations for pairs with equal radii and heights.
Compare a conical snack package with a cylindrical package of equal radius and height, then calculate how much each can hold.
Keep exploring
Related Standards
- 7.8.B
explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and...
- 8.6.A
describe the volume formula V = Bh of a cylinder in terms of its base area and its height
- 7.8.A
model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship...
- 8.7.A
solve problems involving the volume of cylinders, cones, and spheres
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