Surface to Volume Ratio of Pentagonal Trapezohedron given Height Calculator

✖Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.ⓘ Height of Pentagonal Trapezohedron [h]

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✖SA:V of Pentagonal Trapezohedron is the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron.ⓘ Surface to Volume Ratio of Pentagonal Trapezohedron given Height [AV]

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Surface to Volume Ratio of Pentagonal Trapezohedron given Height

Formula

`"AV" = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*("h"/((sqrt(5+2*sqrt(5))))))`

Example

`"0.447214m⁻¹"=((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*("30m"/((sqrt(5+2*sqrt(5))))))`

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Surface to Volume Ratio of Pentagonal Trapezohedron given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5))))))
AV = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(h/((sqrt(5+2*sqrt(5))))))
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 Pentagonal Trapezohedron - (Measured in 1 per Meter) - SA:V of Pentagonal Trapezohedron is the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron.
Height of Pentagonal Trapezohedron - (Measured in Meter) - Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.

STEP 1: Convert Input(s) to Base Unit

Height of Pentagonal Trapezohedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

AV = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(h/((sqrt(5+2*sqrt(5)))))) --> ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(30/((sqrt(5+2*sqrt(5))))))

Evaluating ... ...

AV = 0.447213595499958

STEP 3: Convert Result to Output's Unit

0.447213595499958 1 per Meter --> No Conversion Required

FINAL ANSWER

0.447213595499958 ≈ 0.447214 1 per Meter <-- SA:V of Pentagonal Trapezohedron

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Surface to Volume Ratio of Pentagonal Trapezohedron Calculators

Surface to Volume Ratio of Pentagonal Trapezohedron given Total Surface Area

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5))))))))

Surface to Volume Ratio of Pentagonal Trapezohedron given Height

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5))))))

Surface to Volume Ratio of Pentagonal Trapezohedron given Volume

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3)))

Surface to Volume Ratio of Pentagonal Trapezohedron given Short Edge

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))))

Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2))))

Surface to Volume Ratio of Pentagonal Trapezohedron

Go SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*Antiprism Edge Length of Pentagonal Trapezohedron)

Surface to Volume Ratio of Pentagonal Trapezohedron given Height Formula

What is a Pentagonal Trapezohedron?

In geometry, a Pentagonal Trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. It can be decomposed into two pentagonal pyramids and a pentagonal antiprism in the middle. It can also be decomposed into two pentagonal pyramids and a dodecahedron in the middle.

What is a Trapezohedron?

The n-gonal Trapezohedron, antidipyramid, antibipyramid, or deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of the n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (also called deltoids). The n-gon part of the name does not refer to faces here but to two arrangements of vertices around an axis of symmetry. The dual n-gonal antiprism has two actual n-gon faces. An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.

How to Calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Height?

Surface to Volume Ratio of Pentagonal Trapezohedron given Height calculator uses SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))) to calculate the SA:V of Pentagonal Trapezohedron, Surface to Volume Ratio of Pentagonal Trapezohedron given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron, calculated using its height. SA:V of Pentagonal Trapezohedron is denoted by AV symbol.

How to calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Height using this online calculator? To use this online calculator for Surface to Volume Ratio of Pentagonal Trapezohedron given Height, enter Height of Pentagonal Trapezohedron (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Pentagonal Trapezohedron given Height calculation can be explained with given input values -> 0.447214 = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(30/((sqrt(5+2*sqrt(5)))))).

FAQ

What is Surface to Volume Ratio of Pentagonal Trapezohedron given Height?

Surface to Volume Ratio of Pentagonal Trapezohedron given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron, calculated using its height and is represented as AV = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(h/((sqrt(5+2*sqrt(5)))))) or SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))). Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.

How to calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Height?

Surface to Volume Ratio of Pentagonal Trapezohedron given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Trapezohedron to the volume of the Pentagonal Trapezohedron, calculated using its height is calculated using SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))). To calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Height, you need Height of Pentagonal Trapezohedron (h). With our tool, you need to enter the respective value for Height of Pentagonal Trapezohedron 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 Pentagonal Trapezohedron?

In this formula, SA:V of Pentagonal Trapezohedron uses Height of Pentagonal Trapezohedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*Antiprism Edge Length of Pentagonal Trapezohedron)
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))))
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2))))
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5))))))))
SA:V of Pentagonal Trapezohedron = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3)))

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