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Surface to Volume Ratio of Pentagonal Trapezohedron given Height Formula

GoSurface to Volume Ratio of Pentagonal Trapezohedron Formula

GoSurface to Volume Ratio of Pentagonal Trapezohedron given Short Edge Formula

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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. Check FAQs

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{h}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

AV - SA:V of Pentagonal Trapezohedron?h - Height of Pentagonal Trapezohedron?

Surface to Volume Ratio of Pentagonal Trapezohedron given Height Example

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Here is how the Surface to Volume Ratio of Pentagonal Trapezohedron given Height equation looks like with Values.

Here is how the Surface to Volume Ratio of Pentagonal Trapezohedron given Height equation looks like with Units.

Here is how the Surface to Volume Ratio of Pentagonal Trapezohedron given Height equation looks like.

0.4472 = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{30}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

0.4472m⁻¹ = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{30m}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

0.4472 = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{30}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

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Surface to Volume Ratio of Pentagonal Trapezohedron given Height Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Pentagonal Trapezohedron given Height?

FIRST Step Consider the formula

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{h}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

Next Step Substitute values of Variables

∴

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{30m}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

Next Step Prepare to Evaluate

∴

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{30}{(\sqrt{5 + 2 \cdot \sqrt{5}})})}

Next Step Evaluate

∴

AV = 0.447213595499958m⁻¹

LAST Step Rounding Answer

∴

AV = 0.4472m⁻¹

Surface to Volume Ratio of Pentagonal Trapezohedron given Height Formula Elements

Variables

Functions

SA:V of Pentagonal Trapezohedron

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.

Symbol: AV

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find SA:V of Pentagonal Trapezohedron

Height of Pentagonal Trapezohedron

Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagonal Trapezohedron

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.

Syntax: sqrt(Number)

Other Formulas to find SA:V of Pentagonal Trapezohedron

Go Surface to Volume Ratio of Pentagonal Trapezohedron

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot l e(Antiprism)}

Go Surface to Volume Ratio of Pentagonal Trapezohedron given Short Edge

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{l e(Short)}{(\frac{\sqrt{5} - 1}{2})})}

Go Surface to Volume Ratio of Pentagonal Trapezohedron given Long Edge

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\frac{l e(Long)}{(\frac{\sqrt{5} + 1}{2})})}

Go Surface to Volume Ratio of Pentagonal Trapezohedron given Total Surface Area

AV = \frac{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}{(\frac{5}{12}) \cdot (3 + \sqrt{5}) \cdot (\sqrt{\frac{TSA}{(\sqrt{(\frac{25}{2}) \cdot (5 + \sqrt{5})})}})}

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

Surface to Volume Ratio of Pentagonal Trapezohedron given Height evaluator 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 evaluate 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 evaluate Surface to Volume Ratio of Pentagonal Trapezohedron given Height using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Pentagonal Trapezohedron given Height, enter Height of Pentagonal Trapezohedron (h) and hit the calculate button.

FAQs on Surface to Volume Ratio of Pentagonal Trapezohedron given Height

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

The formula of Surface to Volume Ratio of Pentagonal Trapezohedron given Height is expressed as 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)))))). Here is an example- 0.447214 = ((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*(30/((sqrt(5+2*sqrt(5)))))).

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

With Height of Pentagonal Trapezohedron (h) we can find Surface to Volume Ratio of Pentagonal Trapezohedron given Height using the formula - 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)))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate SA:V of Pentagonal Trapezohedron?

Here are the different ways to Calculate SA:V of Pentagonal Trapezohedron-

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))))

Can the Surface to Volume Ratio of Pentagonal Trapezohedron given Height be negative?

No, the Surface to Volume Ratio of Pentagonal Trapezohedron given Height, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Surface to Volume Ratio of Pentagonal Trapezohedron given Height?

Surface to Volume Ratio of Pentagonal Trapezohedron given Height is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Pentagonal Trapezohedron given Height can be measured.

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