Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume Calculator

✖Volume of Gyroelongated Pentagonal Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Gyroelongated Pentagonal Pyramid.ⓘ Volume of Gyroelongated Pentagonal Pyramid [V]

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✖TSA of Gyroelongated Pentagonal Pyramid is the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Pentagonal Pyramid.ⓘ Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume [SA_Total]

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Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Volume of Gyroelongated Pentagonal Pyramid/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3)
SA_Total = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(V/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(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

TSA of Gyroelongated Pentagonal Pyramid - (Measured in Square Meter) - TSA of Gyroelongated Pentagonal Pyramid is the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Pentagonal Pyramid.
Volume of Gyroelongated Pentagonal Pyramid - (Measured in Cubic Meter) - Volume of Gyroelongated Pentagonal Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Gyroelongated Pentagonal Pyramid.

STEP 1: Convert Input(s) to Base Unit

Volume of Gyroelongated Pentagonal Pyramid: 1900 Cubic Meter --> 1900 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SA_Total = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(V/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3) --> ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(1900/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3)

Evaluating ... ...

SA_Total = 827.326851134049

STEP 3: Convert Result to Output's Unit

827.326851134049 Square Meter --> No Conversion Required

FINAL ANSWER

827.326851134049 ≈ 827.3269 Square Meter <-- TSA of Gyroelongated Pentagonal Pyramid

(Calculation completed in 00.004 seconds)

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< Surface Area of Gyroelongated Pentagonal Pyramid Calculators

Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio

LaTeX Go TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*((((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4)/(((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24)*SA:V of Gyroelongated Pentagonal Pyramid))^2

Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume

LaTeX Go TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Volume of Gyroelongated Pentagonal Pyramid/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3)

Total Surface Area of Gyroelongated Pentagonal Pyramid given Height

LaTeX Go TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))^2

Total Surface Area of Gyroelongated Pentagonal Pyramid

LaTeX Go TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*Edge Length of Gyroelongated Pentagonal Pyramid^2

Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume Formula

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What is a Gyroelongated Pentagonal Pyramid?

The Gyroelongated Pentagonal Pyramid is a regular johnson pentagonal pyramid with a matching antiprism attached to the base, which is the Johnson solid generally denoted by J11. It consists of 16 faces which include 15 equilateral triangles as side surfaces, and a regular pentagon as the base surface. Also, It has 25 edges and 11 vertices.

How to Calculate Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume?

Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume calculator uses TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Volume of Gyroelongated Pentagonal Pyramid/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3) to calculate the TSA of Gyroelongated Pentagonal Pyramid, The Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume formula is defined as the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Pentagonal Pyramid and is calculated using the volume of the Gyroelongated Pentagonal Pyramid. TSA of Gyroelongated Pentagonal Pyramid is denoted by SA_Total symbol.

How to calculate Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume using this online calculator? To use this online calculator for Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume, enter Volume of Gyroelongated Pentagonal Pyramid (V) and hit the calculate button. Here is how the Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume calculation can be explained with given input values -> 827.3269 = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(1900/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3).

FAQ

What is Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume?

The Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume formula is defined as the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Pentagonal Pyramid and is calculated using the volume of the Gyroelongated Pentagonal Pyramid and is represented as SA_Total = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(V/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3) or TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Volume of Gyroelongated Pentagonal Pyramid/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3). Volume of Gyroelongated Pentagonal Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Gyroelongated Pentagonal Pyramid.

How to calculate Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume?

The Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume formula is defined as the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Pentagonal Pyramid and is calculated using the volume of the Gyroelongated Pentagonal Pyramid is calculated using TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Volume of Gyroelongated Pentagonal Pyramid/((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24))^(2/3). To calculate Total Surface Area of Gyroelongated Pentagonal Pyramid given Volume, you need Volume of Gyroelongated Pentagonal Pyramid (V). With our tool, you need to enter the respective value for Volume of Gyroelongated Pentagonal Pyramid 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 TSA of Gyroelongated Pentagonal Pyramid?

In this formula, TSA of Gyroelongated Pentagonal Pyramid uses Volume of Gyroelongated Pentagonal Pyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -

TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*Edge Length of Gyroelongated Pentagonal Pyramid^2
TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*(Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))^2
TSA of Gyroelongated Pentagonal Pyramid = ((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4*((((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4)/(((5*(sqrt(5)+1)*sqrt((10+(2*sqrt(5)))/4-1))/(3*(10-(2*sqrt(5))))+(5+sqrt(5))/24)*SA:V of Gyroelongated Pentagonal Pyramid))^2

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