Free Printable WorksheetMathGeometryMath CurriculumG-GMD.B.4

GEO.170 Solve volume problems with composite 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.170 Solve volume problems with composite solids. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.170 Solve volume problems with composite solids - Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.B.4. Skill statement in this prompt cell: Select the correct decomposition and compute the total volume of a composite solid. Associated standards listed with this skill in the curriculum source: CCSS G-GMD.B.4; FL MA.912.GR.4.1-4.2; VA G.DF.1a. 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.170 Solve volume problems with composite solids skill assessments:

Problem 1Difficulty: Mastery

A pavilion model has a rectangular hall 24 meters by 16 meters by 10 meters, a triangular-prism roof with triangle base 16 meters, triangle height 6 meters, and length 24 meters, a square-pyramid cupola with base side 6 meters and height 5 meters, and a cylindrical skylight hole of radius 2 meters and height 10 meters removed. In terms of pi, which decomposition and volume are correct?

Ahall plus roof plus cupola plus skylight cylinder; 5052 + 40pi cubic meters

Bhall plus roof only; 4992 cubic meters

Croof plus cupola minus skylight; 1212 - 40pi cubic meters

Dhall plus roof plus cupola minus skylight cylinder; 5052 - 40pi cubic meters

Solution & Explanation:The hall volume is 24 x 16 x 10 = 3840. The roof volume is (1/2 x 16 x 6) x 24 = 1152. The cupola volume is (1/3) x 36 x 5 = 60. The skylight hole is pi x 2² x 10 = 40pi. Total volume is 3840 + 1152 + 60 - 40pi = 5052 - 40pi cubic meters.

Problem 2Difficulty: Mastery

A rectangular tank has outer dimensions 15 feet by 10 feet by 6 feet. A rectangular cavity 11 feet by 6 feet by 4 feet is removed, but two cylindrical posts of radius 1 foot and height 6 feet remain inside the cavity. In terms of pi, which decomposition and material volume are correct?

Aouter prism plus cavity plus two cylinders; 1164 + 12pi cubic feet

Bouter prism minus two cylinders only; 900 - 12pi cubic feet

Couter prism minus cavity plus two cylinders; 636 + 12pi cubic feet

Dcavity plus two cylinders only; 264 + 12pi cubic feet

Solution & Explanation:The outer prism volume is 15 x 10 x 6 = 900. The removed cavity is 11 x 6 x 4 = 264. The two posts add 2 x pi x 1² x 6 = 12pi. The material volume is 900 - 264 + 12pi = 636 + 12pi cubic feet.

Problem 3Difficulty: Mastery

A prism has a cross-section made of a 12-unit by 5-unit rectangle and a semicircle with diameter 12 units. The prism length is 7 units. In terms of pi, which decomposition and total volume are correct?

Arectangular prism plus full cylinder; 420 + 252pi cubic units

Brectangular prism plus half-cylinder; 420 + 126pi cubic units

Crectangle plus semicircle area only; 60 + 18pi square units

Dhalf-cylinder only; 126pi cubic units

Solution & Explanation:The rectangular-prism part is 12 x 5 x 7 = 420. The semicircle has radius 6, so the half-cylinder volume is (1/2)pi x 6² x 7 = 126pi. Total volume is 420 + 126pi cubic units.

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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.B.4 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.B.4. Skill statement in this prompt cell: Select the correct decomposition and compute the total volume of a composite solid. Associated standards listed with this skill in the curriculum source: CCSS G-GMD.B.4; FL MA.912.GR.4.1-4.2; VA G.DF.1a. Use this prompt-provided wording as the supporting standard description for this workflow.).