Volume 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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✖Volume of Pentagonal Trapezohedron is the amount of three dimensional space occupied by Pentagonal Trapezohedron.ⓘ Volume of Pentagonal Trapezohedron given Height [V]

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Formula

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Volume of Pentagonal Trapezohedron given Height

Formula

`"V" = (5/12)*(3+sqrt(5))*(("h"/((sqrt(5+2*sqrt(5)))))^3)`

Example

`"2020.626m³"=(5/12)*(3+sqrt(5))*(("30m"/((sqrt(5+2*sqrt(5)))))^3)`

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Volume of Pentagonal Trapezohedron given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))^3)
V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^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

Volume of Pentagonal Trapezohedron - (Measured in Cubic Meter) - Volume of Pentagonal Trapezohedron is the amount of three dimensional space occupied by 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

V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^3) --> (5/12)*(3+sqrt(5))*((30/((sqrt(5+2*sqrt(5)))))^3)

Evaluating ... ...

V = 2020.62589460813

STEP 3: Convert Result to Output's Unit

2020.62589460813 Cubic Meter --> No Conversion Required

FINAL ANSWER

2020.62589460813 ≈ 2020.626 Cubic Meter <-- Volume of Pentagonal Trapezohedron

(Calculation completed in 00.004 seconds)

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< 6 Volume of Pentagonal Trapezohedron Calculators

Volume of Pentagonal Trapezohedron given Surface to Volume Ratio

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

Volume of Pentagonal Trapezohedron given Total Surface Area

Go Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5)))))))^3)

Volume of Pentagonal Trapezohedron given Height

Go Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))^3)

Volume of Pentagonal Trapezohedron given Short Edge

Go Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))^3)

Volume of Pentagonal Trapezohedron given Long Edge

Go Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))^3)

Volume of Pentagonal Trapezohedron

Go Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*(Antiprism Edge Length of Pentagonal Trapezohedron^3)

Volume of Pentagonal Trapezohedron given Height Formula

Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))^3)
V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^3)

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 Volume of Pentagonal Trapezohedron given Height?

Volume of Pentagonal Trapezohedron given Height calculator uses Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))^3) to calculate the Volume of Pentagonal Trapezohedron, The Volume of Pentagonal Trapezohedron given Height formula is defined as the quantity of three-dimensional space enclosed by the Pentagonal Trapezohedron, calculated using its height. Volume of Pentagonal Trapezohedron is denoted by V symbol.

How to calculate Volume of Pentagonal Trapezohedron given Height using this online calculator? To use this online calculator for Volume of Pentagonal Trapezohedron given Height, enter Height of Pentagonal Trapezohedron (h) and hit the calculate button. Here is how the Volume of Pentagonal Trapezohedron given Height calculation can be explained with given input values -> 2020.626 = (5/12)*(3+sqrt(5))*((30/((sqrt(5+2*sqrt(5)))))^3).

FAQ

What is Volume of Pentagonal Trapezohedron given Height?

The Volume of Pentagonal Trapezohedron given Height formula is defined as the quantity of three-dimensional space enclosed by the Pentagonal Trapezohedron, calculated using its height and is represented as V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^3) or Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))^3). Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.

How to calculate Volume of Pentagonal Trapezohedron given Height?

The Volume of Pentagonal Trapezohedron given Height formula is defined as the quantity of three-dimensional space enclosed by the Pentagonal Trapezohedron, calculated using its height is calculated using Volume of Pentagonal Trapezohedron = (5/12)*(3+sqrt(5))*((Height of Pentagonal Trapezohedron/((sqrt(5+2*sqrt(5)))))^3). To calculate Volume 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 Volume of Pentagonal Trapezohedron?

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

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

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