Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height Calculator

✖Height of Gyroelongated Pentagonal Pyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Pentagonal Pyramid.ⓘ Height of Gyroelongated Pentagonal Pyramid [h]

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✖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.ⓘ Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height [AV]

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Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height

Formula

`"AV" = (((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)*"h"/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))`

Example

`"0.429587m⁻¹"=(((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)*"14m"/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))`

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Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Gyroelongated Pentagonal Pyramid = (((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)*Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))
AV = (((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)*h/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))
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

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.
Height of Gyroelongated Pentagonal Pyramid - (Measured in Meter) - Height of Gyroelongated Pentagonal Pyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Pentagonal Pyramid.

STEP 1: Convert Input(s) to Base Unit

Height of Gyroelongated Pentagonal Pyramid: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = (((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)*h/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10))) --> (((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)*14/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))

Evaluating ... ...

AV = 0.4295874285486

STEP 3: Convert Result to Output's Unit

0.4295874285486 1 per Meter --> No Conversion Required

FINAL ANSWER

0.4295874285486 ≈ 0.429587 1 per Meter <-- SA:V of Gyroelongated Pentagonal Pyramid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Johnson Solids » Gyroelongated Pyramids » Gyroelongated Pentagonal Pyramid » Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid » Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height

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< 4 Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid Calculators

Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Volume

Go SA:V of Gyroelongated Pentagonal Pyramid = (((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)*(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))^(1/3))

Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height

Go SA:V of Gyroelongated Pentagonal Pyramid = (((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)*Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10)))

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

Go SA:V of Gyroelongated Pentagonal Pyramid = (((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)*sqrt(TSA of Gyroelongated Pentagonal Pyramid/(((15*sqrt(3))+sqrt(25+(10*sqrt(5))))/4)))

Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid

Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height 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 Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height?

Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height calculator uses SA:V of Gyroelongated Pentagonal Pyramid = (((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)*Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10))) to calculate the SA:V of Gyroelongated Pentagonal Pyramid, The Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height formula is defined as the numerical ratio of the total surface area of the Gyroelongated Pentagonal Pyramid to the volume of the Gyroelongated Pentagonal Pyramid and is calculated using the height of the Gyroelongated Pentagonal Pyramid. SA:V of Gyroelongated Pentagonal Pyramid is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height using this online calculator? To use this online calculator for Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height, enter Height of Gyroelongated Pentagonal Pyramid (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height calculation can be explained with given input values -> 0.429587 = (((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)*14/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10))).

FAQ

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

The Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height formula is defined as the numerical ratio of the total surface area of the Gyroelongated Pentagonal Pyramid to the volume of the Gyroelongated Pentagonal Pyramid and is calculated using the height of the Gyroelongated Pentagonal Pyramid and is represented as AV = (((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)*h/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10))) or SA:V of Gyroelongated Pentagonal Pyramid = (((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)*Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10))). Height of Gyroelongated Pentagonal Pyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Pentagonal Pyramid.

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

The Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height formula is defined as the numerical ratio of the total surface area of the Gyroelongated Pentagonal Pyramid to the volume of the Gyroelongated Pentagonal Pyramid and is calculated using the height of the Gyroelongated Pentagonal Pyramid is calculated using SA:V of Gyroelongated Pentagonal Pyramid = (((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)*Height of Gyroelongated Pentagonal Pyramid/(sqrt(1-4/(10+(2*sqrt(5))))+sqrt((5-sqrt(5))/10))). To calculate Surface to Volume Ratio of Gyroelongated Pentagonal Pyramid given Height, you need Height of Gyroelongated Pentagonal Pyramid (h). With our tool, you need to enter the respective value for Height 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 SA:V of Gyroelongated Pentagonal Pyramid?

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

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

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