A circular cylinder and a sphere share the same radius and equal volumes. What is the cylinder's height________?
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Answer: A. 4/3 times its radius
Explanation
Equating the algebraic volume formula of a cylinder to that of a sphere establishes a direct dimensional relationship. Canceling common terms like pi and radius squared from both sides simplifies the volume equation significantly. Solving the remaining linear expression isolates the cylinder height as equal to four-thirds times its radius. The volume of a circular cylinder is calculated by multiplying the base area by its height dimension. The volume of a three dimensional sphere is given by the standard formula four-thirds pi r cubed. Algebraic balancing allows mathematicians to equate different geometric volume formulas to find missing dimensions.
Option B suggests a height of two-thirds of the radius, which yields a volume smaller than the sphere. Option C proposes a height equal to the radius, failing to satisfy the required volume equality equation. Option D suggests a height equal to the diameter, which creates a cylinder volume exceeding the sphere.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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