What is the volume ratio of a cube to the sphere fitted perfectly inside it________?
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Answer: D. 6: π
Explanation
The volume of a cube with side length a is determined by cubing the side dimension value. A sphere fitted perfectly inside has a radius equal to half of the cube side length. Dividing the cube volume by the sphere volume simplifies algebraically to yield a ratio of six to pi. A sphere inscribed within a cube touches all six faces of the surrounding three dimensional geometric container. The standard mathematical formula for calculating the volume of any sphere is four thirds multiplied by pi r cubed. Ratio simplification involves canceling common algebraic terms present in both the numerator and denominator expressions.
A ratio of four to three ignores the geometric constraints imposed by the inscribed sphere dimensions entirely. The ratio four to two simplifies incorrectly and fails to incorporate the mathematical constant pi in calculations. Four to four represents a simplistic equal proportion that contradicts the actual derived geometric formulas.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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