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Surface to Volume Ratio of Pentagonal Cupola given Height Formula

GoSurface to Volume Ratio of Pentagonal Cupola 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 (\frac{h}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}})}

R_A/V - Surface to Volume Ratio of Pentagonal Cupola?h - Height of Pentagonal Cupola?π - Archimedes' constant?

Surface to Volume Ratio of Pentagonal Cupola given Height Example

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

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

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

0.7501 = \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{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}

0.7501m⁻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 (\frac{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}

0.7501 = \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{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}

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Surface to Volume Ratio of Pentagonal Cupola given Height Solution

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

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

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

Next Step Substitute values of Constants

∴

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{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}

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 (\frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}

Next Step Evaluate

∴

R A/V = 0.750113623648861m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.7501m⁻¹

Surface to Volume Ratio of Pentagonal Cupola given Height Formula Elements

Variables

Constants

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

Height of Pentagonal Cupola

Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagonal Cupola

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

cosec

The cosecant function is a trigonometric function that is the reciprocal of the sine function.

Syntax: cosec(Angle)

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

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}

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 given Height?

Surface to Volume Ratio of Pentagonal Cupola given Height 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)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))) to evaluate the Surface to Volume Ratio of Pentagonal Cupola, The Surface to Volume Ratio of Pentagonal Cupola given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola and is calculated using the height 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 given Height using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Pentagonal Cupola given Height, enter Height of Pentagonal Cupola (h) and hit the calculate button.

FAQs on Surface to Volume Ratio of Pentagonal Cupola given Height

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

The formula of Surface to Volume Ratio of Pentagonal Cupola given Height 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)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))). Here is an example- 0.750114 = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(5/sqrt(1-(1/4*cosec(pi/5)^(2))))).

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

With Height of Pentagonal Cupola (h) we can find Surface to Volume Ratio of Pentagonal Cupola given Height 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)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))). This formula also uses Archimedes' constant and , Secant (sec), Cosecant (cosec), 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)))*Edge Length 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)))*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 given Height be negative?

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

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

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

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