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

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

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

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Formula

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

Formula

`"SA"_{"Total"} = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*"AV"))^2`

Example

`"668.9015m²"=(1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*"0.5m⁻¹"))^2`

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

STEP 0: Pre-Calculation Summary

Formula Used

TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2
SA_Total = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*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 Square Pyramid - (Measured in Square Meter) - TSA of Gyroelongated Square Pyramid is the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Pyramid.
SA:V of Gyroelongated Square Pyramid - (Measured in 1 per Meter) - SA:V of Gyroelongated Square Pyramid is the numerical ratio of the total surface area of the Gyroelongated Square Pyramid to the volume of the Gyroelongated Square Pyramid.

STEP 1: Convert Input(s) to Base Unit

SA:V of Gyroelongated Square Pyramid: 0.5 1 per Meter --> 0.5 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SA_Total = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*AV))^2 --> (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*0.5))^2

Evaluating ... ...

SA_Total = 668.901543260719

STEP 3: Convert Result to Output's Unit

668.901543260719 Square Meter --> No Conversion Required

FINAL ANSWER

668.901543260719 ≈ 668.9015 Square Meter <-- TSA of Gyroelongated Square Pyramid

(Calculation completed in 00.004 seconds)

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< 4 Surface Area of Gyroelongated Square Pyramid Calculators

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

Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2

Total Surface Area of Gyroelongated Square Pyramid given Volume

Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((3*Volume of Gyroelongated Square Pyramid)/(sqrt(4+(3*sqrt(2)))+1/sqrt(2)))^(2/3)

Total Surface Area of Gyroelongated Square Pyramid given Height

Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*(Height of Gyroelongated Square Pyramid/(sqrt(1-1/(2+sqrt(2)))+1/sqrt(2)))^2

Total Surface Area of Gyroelongated Square Pyramid

Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*Edge Length of Gyroelongated Square Pyramid^2

Total Surface Area of Gyroelongated Square Pyramid given Surface to Volume Ratio Formula

What is a Gyroelongated Square Pyramid?

The Gyroelongated Square Pyramid is a regular johnson square pyramid with a matching antiprism attached to the base, which is the Johnson solid generally denoted by J10. It consists of 13 faces which include 12 equilateral triangles as side surfaces, and a square as the base surface. Also, It has 20 edges and 9 vertices.

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

Total Surface Area of Gyroelongated Square Pyramid given Surface to Volume Ratio calculator uses TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2 to calculate the TSA of Gyroelongated Square Pyramid, The Total Surface Area of Gyroelongated Square 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 Square Pyramid and is calculated using the surface to volume ratio of the Gyroelongated Square Pyramid. TSA of Gyroelongated Square Pyramid is denoted by SA_Total symbol.

How to calculate Total Surface Area of Gyroelongated Square Pyramid given Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area of Gyroelongated Square Pyramid given Surface to Volume Ratio, enter SA:V of Gyroelongated Square Pyramid (AV) and hit the calculate button. Here is how the Total Surface Area of Gyroelongated Square Pyramid given Surface to Volume Ratio calculation can be explained with given input values -> 668.9015 = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*0.5))^2.

FAQ

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

The Total Surface Area of Gyroelongated Square 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 Square Pyramid and is calculated using the surface to volume ratio of the Gyroelongated Square Pyramid and is represented as SA_Total = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*AV))^2 or TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2. SA:V of Gyroelongated Square Pyramid is the numerical ratio of the total surface area of the Gyroelongated Square Pyramid to the volume of the Gyroelongated Square Pyramid.

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

The Total Surface Area of Gyroelongated Square 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 Square Pyramid and is calculated using the surface to volume ratio of the Gyroelongated Square Pyramid is calculated using TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2. To calculate Total Surface Area of Gyroelongated Square Pyramid given Surface to Volume Ratio, you need SA:V of Gyroelongated Square Pyramid (AV). With our tool, you need to enter the respective value for SA:V of Gyroelongated Square 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 Square Pyramid?

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

TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*Edge Length of Gyroelongated Square Pyramid^2
TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*(Height of Gyroelongated Square Pyramid/(sqrt(1-1/(2+sqrt(2)))+1/sqrt(2)))^2
TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((3*Volume of Gyroelongated Square Pyramid)/(sqrt(4+(3*sqrt(2)))+1/sqrt(2)))^(2/3)

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