Height Of Hollow Cuboid Given Total Surface Area And Surface To Volume Ratio Calculator

Formula Used:

\[ h = \frac{TSA}{2 \times \frac{RA}{V} \times t \times (l_{Outer} + b_{Outer} - (2 \times t))} \]

Total Surface Area of Hollow Cuboid (TSA):

m²

Surface to Volume Ratio (RA/V):

1/m

Thickness of Hollow Cuboid (t):

Outer Length of Hollow Cuboid (lOuter):

Outer Breadth of Hollow Cuboid (bOuter):

Height of Hollow Cuboid (h):

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1. What is Height of Hollow Cuboid?

The height of a hollow cuboid is the vertical distance between the top and bottom rectangular faces of the hollow cuboidal structure. It represents the perpendicular measurement from the base to the top surface of the hollow cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{TSA}{2 \times \frac{RA}{V} \times t \times (l_{Outer} + b_{Outer} - (2 \times t))} \]

Where:

\( h \) — Height of Hollow Cuboid (m)
\( TSA \) — Total Surface Area of Hollow Cuboid (m²)
\( \frac{RA}{V} \) — Surface to Volume Ratio of Hollow Cuboid (1/m)
\( t \) — Thickness of Hollow Cuboid (m)
\( l_{Outer} \) — Outer Length of Hollow Cuboid (m)
\( b_{Outer} \) — Outer Breadth of Hollow Cuboid (m)

Explanation: This formula calculates the height of a hollow cuboid based on its total surface area, surface to volume ratio, thickness, and outer dimensions.

3. Importance of Height Calculation

Details: Calculating the height of a hollow cuboid is essential for various engineering and architectural applications, including structural design, material estimation, and space optimization in construction projects.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length dimensions, square meters for area, and 1/meter for surface to volume ratio). Ensure all values are positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow cuboid?
A: A hollow cuboid is a three-dimensional shape with six rectangular faces where the inner part is removed, creating a hollow space inside while maintaining the outer cuboidal shape.

Q2: Why is surface to volume ratio important?
A: Surface to volume ratio is crucial in determining various physical properties like heat transfer, chemical reactivity, and structural efficiency of hollow cuboidal structures.

Q3: Can this calculator handle different units?
A: The calculator uses consistent SI units (meters). For other units, convert all measurements to meters before inputting values.

Q4: What if I get undefined result?
A: An undefined result typically occurs when the denominator becomes zero, which happens when the input values create a mathematically impossible scenario.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. The accuracy depends on the precision of your input measurements.