Free Printable WorksheetMathGeometryMath CurriculumG-MG.A.2-3

GEO.179 Use density and rates in geometric modeling Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.179 Use density and rates in geometric modeling. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.179 Use density and rates in geometric modeling - Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.2-3. Skill statement in this prompt cell: Select the correct rate model (such as density or cost per area) and compute the requested quantity with correct units. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.2-3; FL MA.912.GR.4.4-4.5; MA G-MG.A.2-3. 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.179 Use density and rates in geometric modeling skill assessments:

Problem 1Difficulty: Mastery

A concrete border surrounds a square fountain. The outer square is 20 feet on each side, the inner square fountain is 16 feet on each side, and the border is 0.5 foot thick vertically. Concrete weighs 150 pounds per cubic foot and costs $140 per cubic yard. Which pair is correct, with cost rounded to the nearest dollar?

A$187 and 5400 pounds

B$373 and 10800 pounds

C$560 and 10800 pounds

D$1493 and 21600 pounds

Solution & Explanation:The border area is 20² - 16² = 400 - 256 = 144 square feet. Volume is 144 x 0.5 = 72 cubic feet. Weight is 72 x 150 = 10800 pounds. Convert volume to cubic yards: 72 / 27 = 2.666..., and cost is 2.666... x $140 = $373.33, which rounds to $373.

Problem 2Difficulty: Mastery

A rectangular display case is 8 inches by 5 inches by 4 inches. Glass covers all six faces at $0.04 per square inch, and support gel fills the volume at $0.02 per cubic inch. Which pair of costs is correct?

AGlass $3.20 and gel $7.36

BGlass $7.36 and gel $3.20

CGlass $14.72 and gel $3.20

DGlass $7.36 and gel $6.40

Solution & Explanation:Glass uses surface area: 2(8 x 5 + 8 x 4 + 5 x 4) = 184 square inches, so glass cost is 184 x $0.04 = $7.36. Gel uses volume: 8 x 5 x 4 = 160 cubic inches, so gel cost is 160 x $0.02 = $3.20.

Problem 3Difficulty: Mastery

A rug cleaner charges $18 per square yard. A rectangular rug is 15 feet by 9 feet. Which setup and cost use the correct units?

A15 x 9 x 18 = $2430

B(15 x 9 / 9) x 18 = $270

C(2 x 15 + 2 x 9) x 18 = $864

D(15 x 9 / 3) x 18 = $810

Solution & Explanation:The area is 15 x 9 = 135 square feet. Since the rate is per square yard, convert square feet to square yards: 135 / 9 = 15 square yards. The cost is 15 x $18 = $270.

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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-MG.A.2-3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.2-3. Skill statement in this prompt cell: Select the correct rate model (such as density or cost per area) and compute the requested quantity with correct units. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.2-3; FL MA.912.GR.4.4-4.5; MA G-MG.A.2-3. Use this prompt-provided wording as the supporting standard description for this workflow.).