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Area and volume ratios, removed cones and nested shapes
Free examples and worked answers. No account needed.
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Area and volume ratios, removed cones and nested shapes
Area and volume ratios, removed cones and nested shapes
Example 1
Two similar solids have surface areas in the ratio 25:36. The smaller has volume 625cm3. Find the larger volume.
Similar solidsDiagram not to scaleShow worked answer
Answer: 1080
- The linear ratio is 5:6
- the volume ratio is 125:216.
- The larger volume is 1080cm3.
Example 2
Two similar solids have volumes 135cm3 and 320cm3. A corresponding edge in the smaller solid is 12cm. Find the corresponding edge in the larger solid.
Similar solidsDiagram not to scaleShow worked answer
Answer: 16
- Take the cube root of the volume ratio to get 3:4.
- Multiply 12 by 34 to obtain 16cm.
Example 3
Two similar solids have surface areas in the ratio 4:9. The smaller has volume 32cm3. Find the larger volume.
Similar solidsDiagram not to scaleShow worked answer
Answer: 108
- The linear ratio is 2:3
- the volume ratio is 8:27.
- The larger volume is 108cm3.
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