Free Printable WorksheetMathGeometryMath CurriculumG-GMD.A.3

GEO.169 Identify and analyze cross sections of solids Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.169 Identify and analyze cross sections of solids. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.169 Identify and analyze cross sections of solids - Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.A.3. Skill statement in this prompt cell: Select the correct cross section shape for a described slice of a solid. Associated standards listed with this skill in the curriculum source: CCSS G-GMD.A.3; FL MA.912.GR.4.4-4.6; TEKS §111.41(c); VA G.DF.1. 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.169 Identify and analyze cross sections of solids skill assessments:

Problem 1Difficulty: Mastery
A teacher asks for slice descriptions that guarantee circular cross sections. Which set is correct for a sphere, a cylinder, and a cone?
ASphere: any non-tangent plane; cylinder: plane parallel to bases; cone: plane parallel to base
BSphere: plane through one edge; cylinder: plane through axis; cone: plane through vertex
CSphere: vertical plane only; cylinder: any slanted plane; cone: any plane
DSphere: plane parallel to a face; cylinder: plane perpendicular to axis; cone: plane through a base chord only
Solution & Explanation:A sphere sliced by any non-tangent plane forms a circle. A cylinder or cone forms a circle when the slicing plane is parallel to its circular base.
Problem 2Difficulty: Mastery
A rectangular prism fills 0 <= x <= 5, 0 <= y <= 3, and 0 <= z <= 5. A plane z = 1 + 0.4x + 0.2y cuts the four vertical side faces and avoids the top and bottom. What shape is the cross section?
ARectangle
BParallelogram
CTriangle
DCircle
Solution & Explanation:The tilted plane turns the rectangular base footprint into a four-sided section with opposite sides parallel. Because both x and y affect z, the section is a parallelogram rather than a rectangle.
Problem 3Difficulty: Mastery
A right circular cylinder is sliced first by a plane through its axis and then by a slanted plane that cuts only the curved side surface. What are the cross section shapes in order?
ACircle, rectangle
BTriangle, circle
CRectangle, ellipse
DHexagon, triangle
Solution & Explanation:A plane through the cylinder's axis makes a rectangle. A slanted plane through only the curved side makes an ellipse.

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Frequently Asked Questions

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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.3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.A.3. Skill statement in this prompt cell: Select the correct cross section shape for a described slice of a solid. Associated standards listed with this skill in the curriculum source: CCSS G-GMD.A.3; FL MA.912.GR.4.4-4.6; TEKS §111.41(c); VA G.DF.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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