Two spheres have radii in a 1:3 ratio. Find the ratio of their volumes.
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Answer: B. 1:27
Explanation
The volume ratio of two similar three-dimensional spheres equals the cube of the ratio of their radii. Cubing the given radius ratio of one-third yields one over twenty-seven for the volumetric proportion. This mathematical cubic scaling relationship applies universally to all geometrically similar spherical objects. Volume scaling principles dictate that scaling linear dimensions by a factor scales volume by that factor cubed. The mathematical formula for the volume of a sphere is four thirds pi multiplied by radius cubed. Proportions compare dimensional properties of similar geometric shapes without requiring absolute measurement values.
Option A suggests twenty-seven to one which inverts the numerator and denominator of the radius cube ratio. Option C suggests one to nine which incorrectly squares the radius ratio instead of cubing it for volume. Option D suggests nine to one which squares and inverts the radius ratio incorrectly for spherical volumes.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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