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Space Diagonal Formula:
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The space diagonal of a cuboid is the longest straight line that can be drawn from one corner of the cuboid to the opposite corner, passing through its interior. It connects two vertices that are not on the same face.
The calculator uses the space diagonal formula:
Where:
Since height is not directly provided, it's calculated from volume: \[ h = \frac{V}{l \times w} \]
Explanation: The formula is derived from the 3D Pythagorean theorem, where the space diagonal is the hypotenuse of a right triangle whose sides are the length, width, and height of the cuboid.
Details: Calculating the space diagonal is important in various applications including packaging design, construction, 3D modeling, and determining the longest possible object that can fit inside a box or container.
Tips: Enter the length, width, and volume of the cuboid. All values must be positive numbers. The calculator will compute the height from the volume and then calculate the space diagonal.
Q1: What's the difference between space diagonal and face diagonal?
A: Space diagonal connects opposite corners through the 3D space, while face diagonal lies on a single face of the cuboid and connects opposite corners of that face.
Q2: Can the space diagonal be longer than the sum of all three dimensions?
A: Yes, the space diagonal is typically longer than any single dimension and follows the Pythagorean theorem in three dimensions.
Q3: What units should I use for the inputs?
A: Use consistent units for all measurements. The space diagonal will be in the same units as the length and width inputs.
Q4: Does this formula work for all rectangular prisms?
A: Yes, this formula works for all cuboids (rectangular prisms) regardless of their specific dimensions.
Q5: What if my cuboid has zero volume?
A: The calculator requires positive values for all inputs. A cuboid with zero volume doesn't exist in practical terms.