What is the length of the longest rod that fits inside a 4 m cubic room?
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Answer: C. 6.928 m
Explanation
The longest rod inside a three dimensional cube must span diagonally from one bottom corner to the opposite top corner. Multiplying the cube side length by the square root of three yields the exact space diagonal measurement. Calculating four multiplied by approximately one point seven three two gives a length of six point nine two eight meters. The space diagonal of a rectangular cuboid is found using the three dimensional Pythagorean theorem formula. The square root of three is an irrational mathematical constant frequently appearing in three dimensional geometry calculations. A cubic room possesses equal length, breadth, and height dimensions across all of its spatial axes.
Option A incorrectly applies a multiplier that fails to match the proper three dimensional diagonal formula. Option B calculates the face diagonal of a single wall rather than the internal space diagonal. Option D provides an erroneous decimal value resulting from an incorrect radical approximation step.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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