Total Surface Area Of Cuboid Given Space Diagonal, Length And Height Calculator

Formula Used:

\[ Total Surface Area = 2 \times (Length \times Height + Length \times Width + Height \times Width) \] \[ Width = \sqrt{Space Diagonal^2 - Length^2 - Height^2} \]

Total Surface Area:

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1. What is Total Surface Area of Cuboid?

The total surface area of a cuboid is the sum of the areas of all six rectangular faces. It represents the total area that the surface of the cuboid occupies.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ Width = \sqrt{Space Diagonal^2 - Length^2 - Height^2} \] \[ Total Surface Area = 2 \times (Length \times Height + Length \times Width + Height \times Width) \]

Where:

\( Length \) — Length of the cuboid
\( Height \) — Height of the cuboid
\( Space Diagonal \) — Diagonal distance between opposite corners of the cuboid
\( Width \) — Width of the cuboid (calculated from the space diagonal)

Explanation: The calculator first calculates the missing width dimension using the space diagonal formula, then computes the total surface area using all three dimensions.

3. Importance of Surface Area Calculation

Details: Calculating surface area is crucial for various applications including material estimation, packaging design, heat transfer calculations, and construction planning.

4. Using the Calculator

Tips: Enter the length, height, and space diagonal of the cuboid. All values must be positive numbers. The space diagonal must be greater than or equal to the square root of (length² + height²).

5. Frequently Asked Questions (FAQ)

Q1: What is a cuboid?
A: A cuboid is a three-dimensional shape with six rectangular faces, where opposite faces are equal and parallel.

Q2: Why do we need space diagonal to calculate surface area?
A: When only length, height, and space diagonal are known, the width dimension can be derived using the space diagonal formula, allowing complete surface area calculation.

Q3: What are the units for surface area?
A: Surface area is measured in square units (e.g., square meters, square centimeters, square inches) depending on the input units.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q5: What if I get an error message?
A: The error indicates that the space diagonal value is too small relative to the length and height. Please verify your inputs and ensure the space diagonal is valid.