The Cuboid Diagonal Formula: With Example for Students
Learn the trick and formula to quickly and easily calculating a cuboid diagonal. With our clear explanations and useful examples, you can unravel the mysteries and become an expert in the field.
Cuboid Diagonal Formula
The line that joins two of a cuboid’s opposite corners or vertices is called the diagonal. To put it simply, imagine drawing a line from the box’s corner that is closest to you to the corner that is furthest from you.
The Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse—the side opposite the right angle—is equal to the sum of the squares of the other two sides, can be used to calculate the length of a cuboid’s diagonal.
For a cuboid, if the length (l), width (w), and height (h) are known, then the formula to find the diagonal (d) is:
d = √(l² + w² + h²)
In this case, the cuboid’s sides stand for distinct dimensions. The length of the diagonal can be found by entering the lengths of the cuboid’s three dimensions into the formula and performing the required operations (addition and squares).
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For instance, the diagonal of a cuboid with dimensions of 5 units for length, 3 units for width, and 4 units for height can be found using the following formula:
d = √(5² + 3² + 4²) = √(25 + 9 + 16) = √(50) = 7.07 units
Therefore, the cuboid’s diagonal in this example is roughly 7.07 units.
The diagonal’s length can be found using this formula instead of taking a physical measurement. Particularly helpful in a variety of mathematical and engineering contexts, it can be used to compute dimensions, distances, and spatial requirements in three-dimensional spaces.