Area of Pentagon of Truncated Rhombohedron given Volume Calculator

✖Volume of Truncated Rhombohedron is the total quantity of three-dimensional space enclosed by the surface of the Truncated Rhombohedron.ⓘ Volume of Truncated Rhombohedron [V]

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✖Area of Pentagon of Truncated Rhombohedron is the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron.ⓘ Area of Pentagon of Truncated Rhombohedron given Volume [A_Pentagon]

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Formula

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Area of Pentagon of Truncated Rhombohedron given Volume

Formula

`"A"_{"Pentagon"} = ((sqrt(5+(2*sqrt(5))))/4)*(((3*"V")/(5*(sqrt(sqrt(5)-2))))^(2/3))`

Example

`"526.6205m²"=((sqrt(5+(2*sqrt(5))))/4)*(((3*"14500m³")/(5*(sqrt(sqrt(5)-2))))^(2/3))`

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Area of Pentagon of Truncated Rhombohedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3))
A_Pentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((3*V)/(5*(sqrt(sqrt(5)-2))))^(2/3))
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

Area of Pentagon of Truncated Rhombohedron - (Measured in Square Meter) - Area of Pentagon of Truncated Rhombohedron is the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron.
Volume of Truncated Rhombohedron - (Measured in Cubic Meter) - Volume of Truncated Rhombohedron is the total quantity of three-dimensional space enclosed by the surface of the Truncated Rhombohedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Truncated Rhombohedron: 14500 Cubic Meter --> 14500 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Pentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((3*V)/(5*(sqrt(sqrt(5)-2))))^(2/3)) --> ((sqrt(5+(2*sqrt(5))))/4)*(((3*14500)/(5*(sqrt(sqrt(5)-2))))^(2/3))

Evaluating ... ...

A_Pentagon = 526.620521477293

STEP 3: Convert Result to Output's Unit

526.620521477293 Square Meter --> No Conversion Required

FINAL ANSWER

526.620521477293 ≈ 526.6205 Square Meter <-- Area of Pentagon of Truncated Rhombohedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< 7 Area of Pentagon of Truncated Rhombohedron Calculators

Area of Pentagon of Truncated Rhombohedron given Surface to Volume Ratio

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

Area of Pentagon of Truncated Rhombohedron given Total Surface Area

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

Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius

Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2)

Area of Pentagon of Truncated Rhombohedron given Triangular Edge Length

Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)

Area of Pentagon of Truncated Rhombohedron given Volume

Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3))

Area of Pentagon of Truncated Rhombohedron

Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)

Area of Pentagon of Truncated Rhombohedron given Rhombohedral Edge Length

Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(Rhombohedral Edge Length of Truncated Rhombohedron^2)

Area of Pentagon of Truncated Rhombohedron given Volume 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 Area of Pentagon of Truncated Rhombohedron given Volume?

Area of Pentagon of Truncated Rhombohedron given Volume calculator uses Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3)) to calculate the Area of Pentagon of Truncated Rhombohedron, Area of Pentagon of Truncated Rhombohedron given Volume formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron, calculated using its volume. Area of Pentagon of Truncated Rhombohedron is denoted by A_Pentagon symbol.

How to calculate Area of Pentagon of Truncated Rhombohedron given Volume using this online calculator? To use this online calculator for Area of Pentagon of Truncated Rhombohedron given Volume, enter Volume of Truncated Rhombohedron (V) and hit the calculate button. Here is how the Area of Pentagon of Truncated Rhombohedron given Volume calculation can be explained with given input values -> 526.6205 = ((sqrt(5+(2*sqrt(5))))/4)*(((3*14500)/(5*(sqrt(sqrt(5)-2))))^(2/3)).

FAQ

What is Area of Pentagon of Truncated Rhombohedron given Volume?

Area of Pentagon of Truncated Rhombohedron given Volume formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron, calculated using its volume and is represented as A_Pentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((3*V)/(5*(sqrt(sqrt(5)-2))))^(2/3)) or Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3)). Volume of Truncated Rhombohedron is the total quantity of three-dimensional space enclosed by the surface of the Truncated Rhombohedron.

How to calculate Area of Pentagon of Truncated Rhombohedron given Volume?

Area of Pentagon of Truncated Rhombohedron given Volume formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron, calculated using its volume is calculated using Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3)). To calculate Area of Pentagon of Truncated Rhombohedron given Volume, you need Volume of Truncated Rhombohedron (V). With our tool, you need to enter the respective value for Volume 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 Area of Pentagon of Truncated Rhombohedron?

In this formula, Area of Pentagon of Truncated Rhombohedron uses Volume of Truncated Rhombohedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(Rhombohedral Edge Length of Truncated Rhombohedron^2)
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2)
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((2*Total Surface Area of Truncated Rhombohedron)/((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15))))
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*Surface to Volume Ratio of Truncated Rhombohedron))^2)

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