Free Printable WorksheetMathGeometryMath CurriculumG-SRT.A (scaling ideas), G-GMD

GEO.163 Scaling effects on area and volume in similar 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.163 Scaling effects on area and volume in similar solids. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.163 Scaling effects on area and volume in similar solids - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.A (scaling ideas), G-GMD. Skill statement in this prompt cell: Select the correct scaling rule for surface area or volume and compute the missing value for similar solids. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.A (scaling ideas), G-GMD; FL MA.912.GR.4.3; VA G.DF.2. 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.163 Scaling effects on area and volume in similar solids skill assessments:

Problem 1Difficulty: Mastery
A diagram shows two similar award trophies. The shorter trophy is 18 centimeters tall and has coating area 324 square centimeters. The taller trophy is 30 centimeters tall and uses 1,250 cubic centimeters of material. What is the taller trophy's coating area?
A540 square centimeters
B810 square centimeters
C900 square centimeters
D1,500 square centimeters
Solution & Explanation:Coating area is surface area, so use the squared length scale factor. From 18 cm to 30 cm, the linear scale factor is 30/18 = 5/3. Surface area is multiplied by (5/3)2 = 25/9. Then 324 x 25/9 = 900 square centimeters. The volume information is not needed for coating area.
Problem 2Difficulty: Mastery
For a pair of similar solids, the larger volume is 64 times the smaller volume and the larger surface area is 16 times the smaller surface area. Which linear scale factor from the smaller solid to the larger solid matches both facts?
A2
B4
C8
D16
Solution & Explanation:A volume multiplier of 64 gives linear scale factor 4 because 43 = 64. A surface area multiplier of 16 also gives linear scale factor 4 because 42 = 16.
Problem 3Difficulty: Mastery
A similar solid has surface area 69% greater than the original. What are the linear scale factor and the volume multiplier?
Alinear scale factor 1.3; volume multiplier 2.197
Blinear scale factor 1.69; volume multiplier 2.197
Clinear scale factor 1.3; volume multiplier 1.69
Dlinear scale factor 0.69; volume multiplier 0.328509
Solution & Explanation:A 69% increase gives surface area multiplier 1.69. Since 1.69 = 1.32, the linear scale factor is 1.3. The volume multiplier is 1.33 = 2.197.

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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-SRT.A (scaling ideas), G-GMD (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.A (scaling ideas), G-GMD. Skill statement in this prompt cell: Select the correct scaling rule for surface area or volume and compute the missing value for similar solids. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.A (scaling ideas), G-GMD; FL MA.912.GR.4.3; VA G.DF.2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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