Two cubes have sides in a 1:2 ratio. What is the ratio of their volumes__________?
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Answer: C. 1:8
Explanation
The volume ratio of two similar geometric cubes equals the cube of the ratio of their side lengths. Cubing the given side length ratio of one-half yields one over eight for the final volumetric proportion. This cubic scaling relationship applies universally to all three-dimensional cubic geometric structures. Volume scaling principles state that scaling linear dimensions of a cube scales its volume by that factor cubed. The mathematical formula for the volume of a cube is calculated by cubing its side length measurement. Proportions express relative sizes of geometric properties without depending on absolute physical measurements.
Option A suggests one to two which incorrectly uses linear side ratio instead of volumetric cubic ratio. Option B suggests one to four which incorrectly squares the side ratio instead of cubing it for volume. Option D suggests two to one which inverts the numerator and denominator of the cubic side length ratio.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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