Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Truncated Rhombohedron is the numerical ratio of the total surface area of a Truncated Rhombohedron to the volume of the Truncated Rhombohedron.ⓘ Surface to Volume Ratio of Truncated Rhombohedron [R_A/V]

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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 Surface to Volume Ratio [TSA]

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Formula

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Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio

Formula

`"TSA" = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*"R"_{"A/V"}*(5/3)*(sqrt(sqrt(5)-2))))^2)`

Example

`"4979.34m²"=(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*"0.2m⁻¹"*(5/3)*(sqrt(sqrt(5)-2))))^2)`

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Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio 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)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*Surface to Volume Ratio of Truncated Rhombohedron*(5/3)*(sqrt(sqrt(5)-2))))^2)
TSA = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*R_A/V*(5/3)*(sqrt(sqrt(5)-2))))^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.
Surface to Volume Ratio of Truncated Rhombohedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Truncated Rhombohedron is the numerical ratio of the total surface area of a Truncated Rhombohedron to the volume of the Truncated Rhombohedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Truncated Rhombohedron: 0.2 1 per Meter --> 0.2 1 per 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)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*R_A/V*(5/3)*(sqrt(sqrt(5)-2))))^2) --> (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*0.2*(5/3)*(sqrt(sqrt(5)-2))))^2)

Evaluating ... ...

TSA = 4979.34040947386

STEP 3: Convert Result to Output's Unit

4979.34040947386 Square Meter --> No Conversion Required

FINAL ANSWER

4979.34040947386 ≈ 4979.34 Square Meter <-- Total Surface Area of Truncated Rhombohedron

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 7 Surface Area of Truncated Rhombohedron Calculators

Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio

Go Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*Surface to Volume Ratio of Truncated Rhombohedron*(5/3)*(sqrt(sqrt(5)-2))))^2)

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius

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

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 given Area of Pentagon

Go Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(4*Area of Pentagon of Truncated Rhombohedron/(sqrt(5+(2*sqrt(5)))))

Total Surface Area of Truncated Rhombohedron given Volume

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

Total Surface Area of Truncated Rhombohedron

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

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 Surface to Volume Ratio Formula

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 Surface to Volume Ratio?

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

How to calculate Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Truncated Rhombohedron (R_A/V) and hit the calculate button. Here is how the Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio calculation can be explained with given input values -> 4979.34 = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*0.2*(5/3)*(sqrt(sqrt(5)-2))))^2).

FAQ

What is Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio?

Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron, calculated using its surface to volume ratio and is represented as TSA = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*R_A/V*(5/3)*(sqrt(sqrt(5)-2))))^2) or Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*Surface to Volume Ratio of Truncated Rhombohedron*(5/3)*(sqrt(sqrt(5)-2))))^2). Surface to Volume Ratio of Truncated Rhombohedron is the numerical ratio of the total surface area of a Truncated Rhombohedron to the volume of the Truncated Rhombohedron.

How to calculate Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio?

Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron, calculated using its surface to volume ratio is calculated using Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*Surface to Volume Ratio of Truncated Rhombohedron*(5/3)*(sqrt(sqrt(5)-2))))^2). To calculate Total Surface Area of Truncated Rhombohedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Truncated Rhombohedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio of Truncated Rhombohedron. We can use 6 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)
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 = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(4*Area of Pentagon of Truncated Rhombohedron/(sqrt(5+(2*sqrt(5)))))
Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3))

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