Volume Of Cube Given Lateral Surface Area Calculator

Formula Used:

\[ V = \left( \frac{LSA}{4} \right)^{3/2} \]

Volume of Cube (V):

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1. What is Volume of Cube given Lateral Surface Area?

The Volume of Cube given Lateral Surface Area is the total quantity of three dimensional space enclosed by the surface of a Cube, calculated using its lateral surface area.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \left( \frac{LSA}{4} \right)^{3/2} \]

Where:

\( V \) — Volume of Cube (m³)
\( LSA \) — Lateral Surface Area of Cube (m²)

Explanation: The formula derives the volume of a cube from its lateral surface area by first finding the side length and then cubing it.

3. Importance of Volume Calculation

Details: Calculating volume from lateral surface area is important in geometry, architecture, and engineering for determining the capacity or space occupied by cubic structures.

4. Using the Calculator

Tips: Enter the lateral surface area in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is lateral surface area of a cube?
A: Lateral surface area is the area of all the lateral faces (sides) of the cube, excluding the top and bottom faces.

Q2: How is this formula derived?
A: The formula is derived by first finding the side length from lateral surface area (side = √(LSA/4)), then cubing it to get volume.

Q3: What units should I use?
A: Use consistent units - typically square meters for area and cubic meters for volume, though any consistent unit system works.

Q4: Can this formula be used for other shapes?
A: No, this specific formula applies only to cubes due to their equal side lengths and specific geometric properties.

Q5: What if I have the total surface area instead?
A: For total surface area, the formula would be different: V = (TSA/6)^(3/2)