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Surface to Volume Ratio of Pentagonal Cupola Formula

GoSurface to Volume Ratio of Pentagonal Cupola given Height Formula

GoSurface to Volume Ratio of Pentagonal Cupola given Total Surface Area Formula

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Surface to Volume Ratio of Pentagonal Cupola is the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola. Check FAQs

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot l e}

R_A/V - Surface to Volume Ratio of Pentagonal Cupola?l_e - Edge Length of Pentagonal Cupola?

Surface to Volume Ratio of Pentagonal Cupola Example

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

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

Here is how the Surface to Volume Ratio of Pentagonal Cupola equation looks like.

0.7134 = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot 10}

0.7134m⁻¹ = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot 10m}

0.7134 = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot 10}

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Surface to Volume Ratio of Pentagonal Cupola Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Pentagonal Cupola?

FIRST Step Consider the formula

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot l e}

Next Step Substitute values of Variables

∴

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot 10m}

Next Step Prepare to Evaluate

∴

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot 10}

Next Step Evaluate

∴

R A/V = 0.71340044973302m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.7134m⁻¹

Surface to Volume Ratio of Pentagonal Cupola Formula Elements

Variables

Functions

Surface to Volume Ratio of Pentagonal Cupola

Surface to Volume Ratio of Pentagonal Cupola is the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Pentagonal Cupola

Edge Length of Pentagonal Cupola

Edge Length of Pentagonal Cupola is the length of any edge of the Pentagonal Cupola.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Pentagonal Cupola

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 Surface to Volume Ratio of Pentagonal Cupola

Go Surface to Volume Ratio of Pentagonal Cupola given Height

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot (\frac{h}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}})}

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

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot \sqrt{\frac{TSA}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}}}

Go Surface to Volume Ratio of Pentagonal Cupola given Volume

R A/V = \frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{1}{3}}}

How to Evaluate Surface to Volume Ratio of Pentagonal Cupola?

Surface to Volume Ratio of Pentagonal Cupola evaluator uses Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola) to evaluate the Surface to Volume Ratio of Pentagonal Cupola, The Surface to Volume Ratio of Pentagonal Cupola formula is defined as the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola. Surface to Volume Ratio of Pentagonal Cupola is denoted by R_A/V symbol.

How to evaluate Surface to Volume Ratio of Pentagonal Cupola using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Pentagonal Cupola, enter Edge Length of Pentagonal Cupola (l_e) and hit the calculate button.

FAQs on Surface to Volume Ratio of Pentagonal Cupola

What is the formula to find Surface to Volume Ratio of Pentagonal Cupola?

The formula of Surface to Volume Ratio of Pentagonal Cupola is expressed as Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola). Here is an example- 0.7134 = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*10).

How to calculate Surface to Volume Ratio of Pentagonal Cupola?

With Edge Length of Pentagonal Cupola (l_e) we can find Surface to Volume Ratio of Pentagonal Cupola using the formula - Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Surface to Volume Ratio of Pentagonal Cupola?

Here are the different ways to Calculate Surface to Volume Ratio of Pentagonal Cupola-

Surface to Volume Ratio of Pentagonal Cupola=(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2)))))
Surface to Volume Ratio of Pentagonal Cupola=(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*sqrt(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))))
Surface to Volume Ratio of Pentagonal Cupola=(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3))

Can the Surface to Volume Ratio of Pentagonal Cupola be negative?

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

Which unit is used to measure Surface to Volume Ratio of Pentagonal Cupola?

Surface to Volume Ratio of Pentagonal Cupola 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 Cupola can be measured.

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