Reducing a wire's radius to one-third while keeping volume constant increases its length by what factor
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Answer: D. 9 times
Explanation
The volume of a cylinder remains constant because no material is added or removed during the process. Volume is directly proportional to the product of the squared radius and the height of the cylinder. Reducing the radius to one third decreases its squared value to one ninth of the original. Cylindrical volume is calculated using the standard mathematical formula pi multiplied by radius squared and height. Maintaining a constant volume means any reduction in cross sectional area requires a proportional increase in length. Algebraic manipulation shows that multiplying the radius by one third necessitates multiplying length by nine.
An increase by one time represents no change whatsoever in the original length of the wire. Increasing the length by three times would incorrectly assume linear scaling rather than quadratic area scaling. A factor of six times fails to properly account for the squared relationship in circular cross sections.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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