Free Printable WorksheetMathGrade 8Math Curriculum8.G.A.4

8.149 Volume and Surface Area of Similar Solids (Scaling) Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.149 Volume and Surface Area of Similar Solids (Scaling). Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.149 Volume and Surface Area of Similar Solids (Scaling) - If a solid is scaled by a factor k, which option correctly states how the surface area and volume change? (CCSS 8.G.A.4; CCSS 8.G.C.9; CA 8.G.A.4; MA 8.G.A.4)

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

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related 8.149 Volume and Surface Area of Similar Solids (Scaling) skill assessments:

Problem 1Difficulty: Hard
Similar solids A and B have surface areas 36 cm2 and 324 cm2. If solid B has volume 864 cm3, what is the volume of solid A?
Solution & Explanation:The surface area ratio 36:324 simplifies to 1:9, so the linear ratio is 1:3. The volume ratio is then 1:27, and 864 x 1/27 = 32.
Problem 2Difficulty: Hard
A solid is enlarged until its volume is 27 times the original and then each dimension of that enlarged solid is doubled. Compared with the original, what are the total surface area and volume factors?
ASurface area x12 and volume x54
BSurface area x18 and volume x108
CSurface area x36 and volume x216
DSurface area x54 and volume x324
Solution & Explanation:A volume factor of 27 means the first scale factor is 3. Doubling afterward gives an overall scale factor of 6. Then surface area changes by 62 = 36 and volume changes by 63 = 216.
Problem 3Difficulty: Hard
A similar cylinder is made at 0.6 times the original dimensions. If the original cylinder has surface area 250 cm2, what is the new surface area?
Solution & Explanation:The surface area factor is 0.62 = 0.36. Then 250 x 0.36 = 90.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.G.A.4 (Primary standard selected for prompt fields: CCSS 8.G.A.4. Skill statement: If a solid is scaled by a factor k, which option correctly states how the surface area and volume change? Associated standards listed with this skill: CCSS 8.G.A.4; CCSS 8.G.C.9; CA 8.G.A.4; MA 8.G.A.4. Use this embedded wording as the best available supporting standard description for this workflow.).

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