When the similarity ratio is m:n, the volume ratio is m³:n³.
📘 Example ①
Two similar solids have a similarity ratio of 2:3. If the volume of the smaller solid is 16cm³, find the volume of the larger solid.
Answer: Volume ratio = 2³:3³ = 8:27. Larger volume = 16 × (27/8) = 54cm³
Two similar solids have a similarity ratio of 2:3. If the volume of the smaller solid is 16cm³, find the volume of the larger solid.
Answer: Volume ratio = 2³:3³ = 8:27. Larger volume = 16 × (27/8) = 54cm³
💡 Key Point
- Similarity ratio m:n → volume ratio m³:n³
- Do not confuse the area ratio (m²:n²) with the volume ratio (m³:n³).
Practice Problems
- Two solids have a similarity ratio of 3:5. If the volume of the larger solid is 250cm³, find the volume of the smaller solid.
Answer and Explanation
- Answer: 54cm³. Volume ratio=27:125. Smaller volume=250×(27/125)=54.