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

GEO.171 Use similarity to find missing dimensions 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.171 Use similarity to find missing dimensions in similar solids. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.171 Use similarity to find missing dimensions 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 scale factor application and compute a missing length, surface area, or volume 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.171 Use similarity to find missing dimensions in similar solids skill assessments:

Problem 1Difficulty: Mastery
Two similar solids have corresponding edge lengths in the ratio 4:9 from smaller to larger. The larger solid has surface area 405 square units, and the smaller solid has volume 128 cubic units. What are the smaller surface area and the larger volume?
A80 square units and 1458 cubic units
B120 square units and 648 cubic units
C180 square units and 1458 cubic units
D80 square units and 729 cubic units
Solution & Explanation:The surface-area ratio is 42:92 = 16:81, so the smaller area is 405 x 16/81 = 80. The volume ratio is 43:93 = 64:729, so the larger volume is 128 x 729/64 = 1458.
Problem 2Difficulty: Mastery
A small soup bowl holds 250 mL and has rim diameter 10 cm. A similar larger bowl should hold 686 mL. What rim diameter should the larger bowl have?
A12 cm
B14 cm
C16 cm
D18 cm
Solution & Explanation:The volume factor is 686/250 = 343/125 = (7/5)3. The linear scale factor is 7/5, so the larger rim diameter is 10 x 7/5 = 14 cm.
Problem 3Difficulty: Mastery
For a pair of similar solids, the surface-area factor from the first solid to the second solid is 25/16. What is the volume factor from the first solid to the second solid?
A5/4
B25/16
C125/64
D625/256
Solution & Explanation:The linear scale factor is sqrt(25/16) = 5/4. The volume factor is (5/4)3 = 125/64.

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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 scale factor application and compute a missing length, surface area, or volume 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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