Volume of Octahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3
V = sqrt(2)/3*(sqrt(TSA/(2*sqrt(3))))^3
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Volume of Octahedron - (Measured in Cubic Meter) - Volume of Octahedron is the total quantity of three dimensional space enclosed by the entire surface of the Octahedron.
Total Surface Area of Octahedron - (Measured in Square Meter) - Total Surface Area of Octahedron is the total quantity of plane enclosed by the entire surface of the Octahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Octahedron: 350 Square Meter --> 350 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = sqrt(2)/3*(sqrt(TSA/(2*sqrt(3))))^3 --> sqrt(2)/3*(sqrt(350/(2*sqrt(3))))^3
Evaluating ... ...
V = 478.7511995102
STEP 3: Convert Result to Output's Unit
478.7511995102 Cubic Meter --> No Conversion Required
FINAL ANSWER
478.7511995102 478.7512 Cubic Meter <-- Volume of Octahedron
(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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Volume of Octahedron Calculators

Volume of Octahedron given Midsphere Radius
​ LaTeX ​ Go Volume of Octahedron = sqrt(2)/3*(2*Midsphere Radius of Octahedron)^3
Volume of Octahedron given Insphere Radius
​ LaTeX ​ Go Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
Volume of Octahedron
​ LaTeX ​ Go Volume of Octahedron = sqrt(2)/3*Edge Length of Octahedron^3
Volume of Octahedron given Circumsphere Radius
​ LaTeX ​ Go Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3

Volume of Octahedron Calculators

Volume of Octahedron given Total Surface Area
​ LaTeX ​ Go Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3
Volume of Octahedron given Insphere Radius
​ LaTeX ​ Go Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
Volume of Octahedron
​ LaTeX ​ Go Volume of Octahedron = sqrt(2)/3*Edge Length of Octahedron^3
Volume of Octahedron given Circumsphere Radius
​ LaTeX ​ Go Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3

Volume of Octahedron given Total Surface Area Formula

​LaTeX ​Go
Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3
V = sqrt(2)/3*(sqrt(TSA/(2*sqrt(3))))^3

What is an Octahedron?

An Octahedron is a symmetric and closed three dimensional shape with 8 identical equilateral triangular faces. It is a Platonic solid, which has 8 faces, 6 vertices and 12 edges. At each vertex, four equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Volume of Octahedron given Total Surface Area?

Volume of Octahedron given Total Surface Area calculator uses Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3 to calculate the Volume of Octahedron, The Volume of Octahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the total surface area of the Octahedron. Volume of Octahedron is denoted by V symbol.

How to calculate Volume of Octahedron given Total Surface Area using this online calculator? To use this online calculator for Volume of Octahedron given Total Surface Area, enter Total Surface Area of Octahedron (TSA) and hit the calculate button. Here is how the Volume of Octahedron given Total Surface Area calculation can be explained with given input values -> 478.7512 = sqrt(2)/3*(sqrt(350/(2*sqrt(3))))^3.

FAQ

What is Volume of Octahedron given Total Surface Area?
The Volume of Octahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the total surface area of the Octahedron and is represented as V = sqrt(2)/3*(sqrt(TSA/(2*sqrt(3))))^3 or Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3. Total Surface Area of Octahedron is the total quantity of plane enclosed by the entire surface of the Octahedron.
How to calculate Volume of Octahedron given Total Surface Area?
The Volume of Octahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Octahedron and calculated using the total surface area of the Octahedron is calculated using Volume of Octahedron = sqrt(2)/3*(sqrt(Total Surface Area of Octahedron/(2*sqrt(3))))^3. To calculate Volume of Octahedron given Total Surface Area, you need Total Surface Area of Octahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Octahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Volume of Octahedron?
In this formula, Volume of Octahedron uses Total Surface Area of Octahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Volume of Octahedron = sqrt(2)/3*Edge Length of Octahedron^3
  • Volume of Octahedron = 4*sqrt(3)*Insphere Radius of Octahedron^3
  • Volume of Octahedron = (4*Circumsphere Radius of Octahedron^3)/3
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