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

✖SA:V of Gyroelongated Pentagonal Pyramid is the numerical ratio of the total surface area of the Gyroelongated Pentagonal Pyramid to the volume of the Gyroelongated Pentagonal Pyramid.ⓘ SA:V of Gyroelongated Pentagonal Pyramid [AV]

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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 Surface to Volume Ratio [SA_Total]

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

Formula

`"SA"_{"Total"} = ((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)*"AV"))^2`

Example

`"980.402m²"=((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)*"0.4m⁻¹"))^2`

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

STEP 0: Pre-Calculation Summary

Formula Used

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
SA_Total = ((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)*AV))^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

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.
SA:V of Gyroelongated Pentagonal Pyramid - (Measured in 1 per Meter) - SA:V of Gyroelongated Pentagonal Pyramid is the numerical ratio of the total surface area of the Gyroelongated Pentagonal Pyramid to the volume of the Gyroelongated Pentagonal Pyramid.

STEP 1: Convert Input(s) to Base Unit

SA:V of Gyroelongated Pentagonal Pyramid: 0.4 1 per Meter --> 0.4 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SA_Total = ((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)*AV))^2 --> ((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)*0.4))^2

Evaluating ... ...

SA_Total = 980.401968476548

STEP 3: Convert Result to Output's Unit

980.401968476548 Square Meter --> No Conversion Required

FINAL ANSWER

980.401968476548 ≈ 980.402 Square Meter <-- TSA of Gyroelongated Pentagonal Pyramid

(Calculation completed in 00.004 seconds)

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< 4 Surface Area of Gyroelongated Pentagonal Pyramid Calculators

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

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

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

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

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 Surface to Volume Ratio Formula

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 Surface to Volume Ratio?

Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio calculator uses 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 to calculate the TSA of Gyroelongated Pentagonal Pyramid, The Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio 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 surface to volume ratio 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 Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio, enter SA:V of Gyroelongated Pentagonal Pyramid (AV) and hit the calculate button. Here is how the Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio calculation can be explained with given input values -> 980.402 = ((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)*0.4))^2.

FAQ

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

The Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio 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 surface to volume ratio of the Gyroelongated Pentagonal Pyramid and is represented as SA_Total = ((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)*AV))^2 or 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. SA:V of Gyroelongated Pentagonal Pyramid is the numerical ratio of the total surface area of the Gyroelongated Pentagonal Pyramid to the volume of the Gyroelongated Pentagonal Pyramid.

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

The Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio 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 surface to volume ratio of the Gyroelongated Pentagonal Pyramid is calculated using 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. To calculate Total Surface Area of Gyroelongated Pentagonal Pyramid given Surface to Volume Ratio, you need SA:V of Gyroelongated Pentagonal Pyramid (AV). With our tool, you need to enter the respective value for SA:V 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 SA:V 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*(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)

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