10.11Similar Solids and Scale Factors
Quick Answer
For similar solids with scale factor k: the ratio of surface areas is k², and the ratio of volumes is k³. Doubling all dimensions multiplies surface area by 4 and volume by 8.
Essential Question
Why does scaling a solid by factor k multiply its surface area by k² and its volume by k³?
Learning Goals
- 1Define similar solids.
- 2State the surface area ratio theorem for similar solids.
- 3State the volume ratio theorem for similar solids.
- 4Find missing surface areas or volumes using scale factor relationships.
- 5Solve applied problems involving similar solids.
Key Vocabulary
Similar solids
Solids with the same shape and proportional dimensions.
Scale factor (k)
The ratio of corresponding linear dimensions of two similar solids.
Surface area ratio
For similar solids with scale factor k, the ratio of surface areas is k².
Volume ratio
For similar solids with scale factor k, the ratio of volumes is k³.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.