Solve comprehensive problems involving similarity ratios, area ratios, volume ratios, and scale drawings.
📘 Example ① (Connection Between Area and Volume)
Two similar solids have a surface-area ratio of 4:9. Find the similarity ratio and volume ratio.
Answer: Area ratio = m²:n² = 4:9 → m:n = 2:3. Volume ratio = 2³:3³ = 8:27
Two similar solids have a surface-area ratio of 4:9. Find the similarity ratio and volume ratio.
Answer: Area ratio = m²:n² = 4:9 → m:n = 2:3. Volume ratio = 2³:3³ = 8:27
💡 Key Point
- Similarity ratio m:n → area ratio m²:n² → volume ratio m³:n³
- If any one of these is known, the others can also be found.
Practice Problems
- Two similar solids have a volume ratio of 8:125. Find the similarity ratio and surface-area ratio.
Answer and Explanation
- Answer: Similarity ratio 2:5, surface-area ratio 4:25. Volume ratio 8:125 = 2³:5³ → similarity ratio 2:5. Area ratio=4:25.