Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Truncated Rhombohedron [r_c]

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

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Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2)
TSA = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*r_c)/(sqrt(14-(2*sqrt(5)))))^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 Truncated Rhombohedron - (Measured in Square Meter) - Total Surface Area of Truncated Rhombohedron is the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron.
Circumsphere Radius of Truncated Rhombohedron - (Measured in Meter) - Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Truncated Rhombohedron: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*r_c)/(sqrt(14-(2*sqrt(5)))))^2) --> (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*20)/(sqrt(14-(2*sqrt(5)))))^2)

Evaluating ... ...

TSA = 3408.05466040375

STEP 3: Convert Result to Output's Unit

3408.05466040375 Square Meter --> No Conversion Required

FINAL ANSWER

3408.05466040375 ≈ 3408.055 Square Meter <-- Total Surface Area of Truncated Rhombohedron

(Calculation completed in 00.020 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Surface Area of Truncated Rhombohedron Calculators

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius

LaTeX Go Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2)

Total Surface Area of Truncated Rhombohedron given Triangular Edge Length

LaTeX Go Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)

Total Surface Area of Truncated Rhombohedron

LaTeX Go Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)

Total Surface Area of Truncated Rhombohedron given Rhombohedral Edge Length

LaTeX Go Total Surface Area of Truncated Rhombohedron = ((Rhombohedral Edge Length of Truncated Rhombohedron^2)*((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15))))/2

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Formula

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What is Truncated Rhombohedron?

The Truncated Rhombohedron is a convex, octahedral polyhedron. It is made up of six equal, irregular, but axially symmetrical pentagons and two equilateral triangles. It has twelve corners; three faces meet at each corner (a triangle and two pentagons or three pentagons). All corner points lie on the same sphere. Opposite faces are parallel. In the stitch, the body stands on a triangular surface, the pentagons virtually form the surface. The number of edges is eighteen.

How to Calculate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius calculator uses Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2) to calculate the Total Surface Area of Truncated Rhombohedron, Total Surface Area of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron, calculated using its circumsphere radius. Total Surface Area of Truncated Rhombohedron is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Truncated Rhombohedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Rhombohedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Truncated Rhombohedron given Circumsphere Radius calculation can be explained with given input values -> 3408.055 = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*20)/(sqrt(14-(2*sqrt(5)))))^2).

FAQ

What is Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron, calculated using its circumsphere radius and is represented as TSA = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*r_c)/(sqrt(14-(2*sqrt(5)))))^2) or Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2). Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

How to calculate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron, calculated using its circumsphere radius is calculated using Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2). To calculate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Rhombohedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Truncated Rhombohedron 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 Truncated Rhombohedron?

In this formula, Total Surface Area of Truncated Rhombohedron uses Circumsphere Radius of Truncated Rhombohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Truncated Rhombohedron = ((Rhombohedral Edge Length of Truncated Rhombohedron^2)*((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15))))/2
Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)
Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)

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