Total Surface Area of Octahedron given Midsphere Radius Calculator

✖Midsphere Radius of Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.ⓘ Midsphere Radius of Octahedron [r_m]

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✖Total Surface Area of Octahedron is the total quantity of plane enclosed by the entire surface of the Octahedron.ⓘ Total Surface Area of Octahedron given Midsphere Radius [TSA]

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Formula

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Total Surface Area of Octahedron given Midsphere Radius

Formula

`"TSA" = 8*sqrt(3)*"r"_{"m"}^2`

Example

`"346.4102m²"=8*sqrt(3)*("5m")^2`

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Total Surface Area of Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2
TSA = 8*sqrt(3)*r_m^2
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

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.
Midsphere Radius of Octahedron - (Measured in Meter) - Midsphere Radius of Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Octahedron: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 8*sqrt(3)*r_m^2 --> 8*sqrt(3)*5^2

Evaluating ... ...

TSA = 346.410161513775

STEP 3: Convert Result to Output's Unit

346.410161513775 Square Meter --> No Conversion Required

FINAL ANSWER

346.410161513775 ≈ 346.4102 Square Meter <-- Total Surface Area of Octahedron

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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Vellore Institute of Technology (VIT), Bhopal

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< 7 Total Surface Area of Octahedron Calculators

Total Surface Area of Octahedron given Volume

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

Total Surface Area of Octahedron given Surface to Volume Ratio

Go Total Surface Area of Octahedron = (108*sqrt(3))/(Surface to Volume Ratio of Octahedron^2)

Total Surface Area of Octahedron given Circumsphere Radius

Go Total Surface Area of Octahedron = 4*sqrt(3)*Circumsphere Radius of Octahedron^2

Total Surface Area of Octahedron given Midsphere Radius

Go Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2

Total Surface Area of Octahedron given Insphere Radius

Go Total Surface Area of Octahedron = 12*sqrt(3)*Insphere Radius of Octahedron^2

Total Surface Area of Octahedron given Space Diagonal

Go Total Surface Area of Octahedron = sqrt(3)*Space Diagonal of Octahedron^2

Total Surface Area of Octahedron

Go Total Surface Area of Octahedron = 2*sqrt(3)*Edge Length of Octahedron^2

< 4 Total Surface Area of Octahedron Calculators

Total Surface Area of Octahedron given Circumsphere Radius

Go Total Surface Area of Octahedron = 4*sqrt(3)*Circumsphere Radius of Octahedron^2

Total Surface Area of Octahedron given Midsphere Radius

Go Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2

Total Surface Area of Octahedron given Space Diagonal

Go Total Surface Area of Octahedron = sqrt(3)*Space Diagonal of Octahedron^2

Total Surface Area of Octahedron

Go Total Surface Area of Octahedron = 2*sqrt(3)*Edge Length of Octahedron^2

Total Surface Area of Octahedron given Midsphere Radius Formula

Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2
TSA = 8*sqrt(3)*r_m^2

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 Total Surface Area of Octahedron given Midsphere Radius?

Total Surface Area of Octahedron given Midsphere Radius calculator uses Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2 to calculate the Total Surface Area of Octahedron, Total Surface Area of Octahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Octahedron, and calculated using the midsphere radius of the Octahedron. Total Surface Area of Octahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Octahedron given Midsphere Radius, enter Midsphere Radius of Octahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Octahedron given Midsphere Radius calculation can be explained with given input values -> 346.4102 = 8*sqrt(3)*5^2.

FAQ

What is Total Surface Area of Octahedron given Midsphere Radius?

Total Surface Area of Octahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Octahedron, and calculated using the midsphere radius of the Octahedron and is represented as TSA = 8*sqrt(3)*r_m^2 or Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2. Midsphere Radius of Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.

How to calculate Total Surface Area of Octahedron given Midsphere Radius?

Total Surface Area of Octahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Octahedron, and calculated using the midsphere radius of the Octahedron is calculated using Total Surface Area of Octahedron = 8*sqrt(3)*Midsphere Radius of Octahedron^2. To calculate Total Surface Area of Octahedron given Midsphere Radius, you need Midsphere Radius of Octahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius 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 Total Surface Area of Octahedron?

In this formula, Total Surface Area of Octahedron uses Midsphere Radius of Octahedron. We can use 9 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Octahedron = 2*sqrt(3)*Edge Length of Octahedron^2
Total Surface Area of Octahedron = 4*sqrt(3)*Circumsphere Radius of Octahedron^2
Total Surface Area of Octahedron = 12*sqrt(3)*Insphere Radius of Octahedron^2
Total Surface Area of Octahedron = sqrt(3)*Space Diagonal of Octahedron^2
Total Surface Area of Octahedron = (108*sqrt(3))/(Surface to Volume Ratio of Octahedron^2)
Total Surface Area of Octahedron = 2*sqrt(3)*((3*Volume of Octahedron)/sqrt(2))^(2/3)
Total Surface Area of Octahedron = 2*sqrt(3)*Edge Length of Octahedron^2
Total Surface Area of Octahedron = 4*sqrt(3)*Circumsphere Radius of Octahedron^2
Total Surface Area of Octahedron = sqrt(3)*Space Diagonal of Octahedron^2

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