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Edge Length of Pentagonal Cupola given Surface to Volume Ratio Formula

GoEdge Length of Pentagonal Cupola given Height Formula

GoEdge Length of Pentagonal Cupola given Total Surface Area Formula

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

l e = \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 R A/V}

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

Edge Length of Pentagonal Cupola given Surface to Volume Ratio Example

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

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

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

10.1914 = \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 0.7}

10.1914m = \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 0.7m⁻¹}

10.1914 = \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 0.7}

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Edge Length of Pentagonal Cupola given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

l e = \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 R A/V}

Next Step Substitute values of Variables

∴

l e = \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 0.7m⁻¹}

Next Step Prepare to Evaluate

∴

l e = \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 0.7}

Next Step Evaluate

∴

l e = 10.191434996186m

LAST Step Rounding Answer

∴

l e = 10.1914m

Edge Length of Pentagonal Cupola given Surface to Volume Ratio Formula Elements

Variables

Functions

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

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

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 Edge Length of Pentagonal Cupola

Go Edge Length of Pentagonal Cupola given Height

l e = \frac{h}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}}

Go Edge Length of Pentagonal Cupola given Total Surface Area

l e = \sqrt{\frac{TSA}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}}

Go Edge Length of Pentagonal Cupola given Volume

l e = {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{1}{3}}

How to Evaluate Edge Length of Pentagonal Cupola given Surface to Volume Ratio?

Edge Length of Pentagonal Cupola given Surface to Volume Ratio evaluator uses Edge Length of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola) to evaluate the Edge Length of Pentagonal Cupola, The Edge Length of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the length of any edge of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola. Edge Length of Pentagonal Cupola is denoted by l_e symbol.

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

FAQs on Edge Length of Pentagonal Cupola given Surface to Volume Ratio

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

The formula of Edge Length of Pentagonal Cupola given Surface to Volume Ratio is expressed as Edge Length of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola). Here is an example- 10.19143 = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*0.7).

How to calculate Edge Length of Pentagonal Cupola given Surface to Volume Ratio?

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

What are the other ways to Calculate Edge Length of Pentagonal Cupola?

Here are the different ways to Calculate Edge Length of Pentagonal Cupola-

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

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

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

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

Edge Length of Pentagonal Cupola given Surface to Volume Ratio is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Edge Length of Pentagonal Cupola given Surface to Volume Ratio can be measured.

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