Two cylinders share an identical height, and their radii maintain a 1: 3 proportion. Given that the initial cylinder possesses a 40 cc volume, calculate the capacity of the second cylinder?
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Answer: A. 360 cc
Explanation
Cylinder volume varies directly as the square of its radius when the height remains constant. Squaring the given radius proportion of one to three yields a volumetric scaling ratio of one to nine. Multiplying the initial cylinder volume of forty cubic centimeters by nine gives three hundred sixty cubic centimeters. The volume of a right circular cylinder equals pi multiplied by radius squared and multiplied by height. Direct proportionality principles state that scaling linear dimensions scales volumetric capacity quadratically for radius. Cubic centimeters are standard metric units used for measuring three-dimensional liquid and solid capacities.
Industrial engineers calculate storage tank capacities when scaling up cylindrical vessel diameters proportionally. Manufacturing technicians determine fluid reservoir volumes when redesigning hydraulic cylinder dimensions. Packaging designers compute container volume changes when scaling cylindrical product packaging proportions. Option B suggests sixty cubic centimeters which represents an incorrect calculation from the radius ratio. Option C suggests three hundred cubic centimeters which results from an arithmetic miscalculation of scaling. Option D suggests thirty-six cubic centimeters which incorrectly scales the volume downward instead of up.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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