A cuboid has edges measuring 3 cm, 4 cm, and 12 cm. Determine its diagonal length.
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Answer: C. 13 cm
Explanation
The diagonal of a rectangular cuboid is calculated using the square root of the sum of squared edge lengths. Squaring the edge lengths three, four, and twelve gives nine, sixteen, and one hundred forty-four. Adding these squared values gives one sixty-nine, and taking its square root results in a diagonal length of thirteen centimeters. The three-dimensional diagonal formula extends Pythagorean theorem principles to cuboids and boxes. Edge lengths represent the orthogonal length, width, and height dimensions of the solid rectangular box. The square root of one sixty-nine evaluates to an exact integer value of thirteen.
Architects and packaging designers calculate spatial diagonals to determine maximum item lengths fitting inside boxes. Physics students use three-dimensional vectors to find resultant displacements in space. Mastering spatial geometry formulas is essential for solving multi-dimensional measurement problems. Option A represents just the hypotenuse of the base face rather than the full three-dimensional diagonal. Option B results from an incorrect arithmetic addition of the squared edge length values. Option D mistakes the sum of squared edges for the final square root diagonal calculation.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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