Free Printable WorksheetMathGeometryMath CurriculumG-GMD.A.1-2 (+)

GEO.162 Cavalieri's Principle and Volume Comparison Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.162 Cavalieri's Principle and Volume Comparison. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.162 Cavalieri's principle and volume comparison - Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.A.1-2 (+). Skill statement in this prompt cell: Select the statement that correctly applies Cavalieri's principle to compare volumes of two solids. Associated standards listed with this skill in the curriculum source: CCSS G-GMD.A.1-2 (+); FL MA.912.GR.4.5 (Cavalieri). Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.162 Cavalieri's Principle and Volume Comparison skill assessments:

Problem 1Difficulty: Mastery

A designer shears a solid by moving each horizontal cross-section sideways. The total height is unchanged, and every cross-section keeps its original area at the same height. Which statement is the correct Cavalieri comparison with the original solid?

AThe sheared solid has equal volume to the original because corresponding slice areas and height are unchanged.

BThe sheared solid has greater volume because its side surface is longer.

CThe sheared solid has less volume because its base is displaced.

DThe volumes cannot be compared unless the surface areas are equal.

Solution & Explanation:Shearing moves slices but does not change their areas or the height interval. Cavalieri's principle shows the sheared solid and original solid have equal volume.

Problem 2Difficulty: Mastery

Two solids have the same height. At every corresponding height, the smaller solid's cross-sectional area is 5/8 of the larger solid's cross-sectional area. If the larger solid has volume 320 cubic units, which statement is correct?

AThe smaller solid has volume 200 cubic units.

BThe smaller solid has volume 512 cubic units.

CThe smaller solid has volume 315 cubic units.

DThe solids have equal volume because their heights are equal.

Solution & Explanation:A constant cross-sectional area ratio of 5/8 throughout the same height gives the same volume ratio. The smaller volume is (5/8) x 320 = 200 cubic units.

Problem 3Difficulty: Mastery

Solids U and V have the same height of 10 units. At every height h, U's cross-sectional area is 2h + 5 square units and V's is 2h + 9 square units. Which statement correctly applies Cavalieri's principle?

AU and V have equal volume because the formulas have the same slope.

BV has 40 cubic units more volume than U.

CU has 40 cubic units more volume than V.

DNo comparison can be made because h changes.

Solution & Explanation:At every height, V's slice area is 4 square units greater than U's. Over a height of 10 units, the volume difference is 4 x 10 = 40 cubic units, so V is larger.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-GMD.A.1-2 (+) (Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.A.1-2 (+). Skill statement in this prompt cell: Select the statement that correctly applies Cavalieri's principle to compare volumes of two solids. Associated standards listed with this skill in the curriculum source: CCSS G-GMD.A.1-2 (+); FL MA.912.GR.4.5 (Cavalieri). Use this prompt-provided wording as the supporting standard description for this workflow.).