Total Surface Area of Cuboctahedron given Midsphere Radius Calculator

✖Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.ⓘ Midsphere Radius of Cuboctahedron [r_m]

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✖Total Surface Area of Cuboctahedron is defined as the measure of the total amount of two-dimensional space enclosed by all the faces of the Cuboctahedron.ⓘ Total Surface Area of Cuboctahedron given Midsphere Radius [TSA]

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Total Surface Area of Cuboctahedron given Midsphere Radius

Formula

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

Example

`"1022.123m²"=2*(3+sqrt(3))*(2/sqrt(3)*"9m")^2`

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Total Surface Area of Cuboctahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^2
TSA = 2*(3+sqrt(3))*(2/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 Cuboctahedron - (Measured in Square Meter) - Total Surface Area of Cuboctahedron is defined as the measure of the total amount of two-dimensional space enclosed by all the faces of the Cuboctahedron.
Midsphere Radius of Cuboctahedron - (Measured in Meter) - Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Cuboctahedron: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 2*(3+sqrt(3))*(2/sqrt(3)*r_m)^2 --> 2*(3+sqrt(3))*(2/sqrt(3)*9)^2

Evaluating ... ...

TSA = 1022.12297443488

STEP 3: Convert Result to Output's Unit

1022.12297443488 Square Meter --> No Conversion Required

FINAL ANSWER

1022.12297443488 ≈ 1022.123 Square Meter <-- Total Surface Area of Cuboctahedron

(Calculation completed in 00.004 seconds)

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Mumbai University (DJSCE), Mumbai

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< 7 Total Surface Area of Cuboctahedron Calculators

Total Surface Area of Cuboctahedron given Surface to Volume Ratio

Go Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*((18+(6*sqrt(3)))/(5*sqrt(2)*Surface to Volume Ratio of Cuboctahedron))^2

Total Surface Area of Cuboctahedron given Lateral Surface Area

Go Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Lateral Surface Area of Cuboctahedron/((2*sqrt(3))+4)

Total Surface Area of Cuboctahedron given Midsphere Radius

Go Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^2

Total Surface Area of Cuboctahedron given Volume

Go Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*((3*Volume of Cuboctahedron)/(5*sqrt(2)))^(2/3)

Total Surface Area of Cuboctahedron given Circumsphere Radius

Go Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Circumsphere Radius of Cuboctahedron^2

Total Surface Area of Cuboctahedron given Perimeter

Go Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Perimeter of Cuboctahedron^2/576

Total Surface Area of Cuboctahedron

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

Total Surface Area of Cuboctahedron given Midsphere Radius Formula

Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^2
TSA = 2*(3+sqrt(3))*(2/sqrt(3)*r_m)^2

What is a Cuboctahedron?

A Cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is the only radially equilateral convex polyhedron.

How to Calculate Total Surface Area of Cuboctahedron given Midsphere Radius?

Total Surface Area of Cuboctahedron given Midsphere Radius calculator uses Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^2 to calculate the Total Surface Area of Cuboctahedron, The Total Surface Area of Cuboctahedron given Midsphere Radius formula is defined as the measure of the total amount of two-dimensional space enclosed by all the faces of the Cuboctahedron, calculated using midsphere radius of Cuboctahedron. Total Surface Area of Cuboctahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Cuboctahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Cuboctahedron given Midsphere Radius, enter Midsphere Radius of Cuboctahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Cuboctahedron given Midsphere Radius calculation can be explained with given input values -> 1022.123 = 2*(3+sqrt(3))*(2/sqrt(3)*9)^2.

FAQ

What is Total Surface Area of Cuboctahedron given Midsphere Radius?

The Total Surface Area of Cuboctahedron given Midsphere Radius formula is defined as the measure of the total amount of two-dimensional space enclosed by all the faces of the Cuboctahedron, calculated using midsphere radius of Cuboctahedron and is represented as TSA = 2*(3+sqrt(3))*(2/sqrt(3)*r_m)^2 or Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^2. Midsphere Radius of Cuboctahedron is the radius of the sphere which is tangent to every edge of the Cuboctahedron and also is present in between its insphere and the circumsphere.

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

The Total Surface Area of Cuboctahedron given Midsphere Radius formula is defined as the measure of the total amount of two-dimensional space enclosed by all the faces of the Cuboctahedron, calculated using midsphere radius of Cuboctahedron is calculated using Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*(2/sqrt(3)*Midsphere Radius of Cuboctahedron)^2. To calculate Total Surface Area of Cuboctahedron given Midsphere Radius, you need Midsphere Radius of Cuboctahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Cuboctahedron 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 Cuboctahedron?

In this formula, Total Surface Area of Cuboctahedron uses Midsphere Radius of Cuboctahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Edge Length of Cuboctahedron^2
Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Circumsphere Radius of Cuboctahedron^2
Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Lateral Surface Area of Cuboctahedron/((2*sqrt(3))+4)
Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*((18+(6*sqrt(3)))/(5*sqrt(2)*Surface to Volume Ratio of Cuboctahedron))^2
Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*((3*Volume of Cuboctahedron)/(5*sqrt(2)))^(2/3)
Total Surface Area of Cuboctahedron = 2*(3+sqrt(3))*Perimeter of Cuboctahedron^2/576

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