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Edge Length of Antiprism given Surface to Volume Ratio Formula

GoEdge Length of Antiprism Formula

GoEdge Length of Antiprism given Total Surface Area Formula

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Edge Length of Antiprism is defined as the straight line joining the adjacent vertices of the Antiprism. Check FAQs

l e = \frac{6 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}{\sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1} \cdot R A/V}

l_e - Edge Length of Antiprism?N_Vertices - Number of Vertices of Antiprism?R_A/V - Surface to Volume Ratio of Antiprism?π - Archimedes' constant?

Edge Length of Antiprism given Surface to Volume Ratio Example

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

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

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

9.845 = \frac{6 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}{\sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot 0.5}

9.845m = \frac{6 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}{\sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot 0.5m⁻¹}

9.845 = \frac{6 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}{\sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot 0.5}

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Edge Length of Antiprism given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

l e = \frac{6 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}{\sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1} \cdot R A/V}

Next Step Substitute values of Variables

∴

l e = \frac{6 \cdot {(\sin (\frac{π}{5}))}^{2} \cdot (\cot (\frac{π}{5}) + \sqrt{3})}{\sin (\frac{3 \cdot π}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot 5})}^{2}) - 1} \cdot 0.5m⁻¹}

Next Step Substitute values of Constants

∴

l e = \frac{6 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}{\sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot 0.5m⁻¹}

Next Step Prepare to Evaluate

∴

l e = \frac{6 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}{\sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot 0.5}

Next Step Evaluate

∴

l e = 9.84497924060948m

LAST Step Rounding Answer

∴

l e = 9.845m

Edge Length of Antiprism given Surface to Volume Ratio Formula Elements

Variables

Constants

Functions

Edge Length of Antiprism

Edge Length of Antiprism is defined as the straight line joining the adjacent vertices of the Antiprism.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Antiprism

Number of Vertices of Antiprism

Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.

Symbol: N_Vertices

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Vertices of Antiprism

Surface to Volume Ratio of Antiprism

Surface to Volume Ratio of Antiprism is the fraction of the surface area to volume of Antiprism.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Antiprism

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(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 Edge Length of Antiprism

Go Edge Length of Antiprism

l e = \frac{h}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}}}

Go Edge Length of Antiprism given Total Surface Area

l e = \sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}}

Go Edge Length of Antiprism given Volume

l e = {(\frac{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot V}{N Vertices \cdot \sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1}})}^{\frac{1}{3}}

How to Evaluate Edge Length of Antiprism given Surface to Volume Ratio?

Edge Length of Antiprism given Surface to Volume Ratio evaluator uses Edge Length of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Surface to Volume Ratio of Antiprism) to evaluate the Edge Length of Antiprism, The Edge Length of Antiprism given Surface to Volume Ratio formula is defined as the straight line joining two adjacent vertices of Antiprism, calculated using surface to volume ratio of Antiprism. Edge Length of Antiprism is denoted by l_e symbol.

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

FAQs on Edge Length of Antiprism given Surface to Volume Ratio

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

The formula of Edge Length of Antiprism given Surface to Volume Ratio is expressed as Edge Length of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Surface to Volume Ratio of Antiprism). Here is an example- 9.844979 = (6*(sin(pi/5))^2*(cot(pi/5)+sqrt(3)))/(sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*0.5).

How to calculate Edge Length of Antiprism given Surface to Volume Ratio?

With Number of Vertices of Antiprism (N_Vertices) & Surface to Volume Ratio of Antiprism (R_A/V) we can find Edge Length of Antiprism given Surface to Volume Ratio using the formula - Edge Length of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Surface to Volume Ratio of Antiprism). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Edge Length of Antiprism?

Here are the different ways to Calculate Edge Length of Antiprism-

Edge Length of Antiprism=Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))
Edge Length of Antiprism=sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))))
Edge Length of Antiprism=((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3)

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

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

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

Edge Length of Antiprism 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 Antiprism given Surface to Volume Ratio can be measured.

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Edge Length of Antiprism given Surface to Volume Ratio Formula

​GoEdge Length of Antiprism Formula

​GoEdge Length of Antiprism given Total Surface Area Formula

Edge Length of Antiprism given Surface to Volume Ratio Example

Edge Length of Antiprism given Surface to Volume Ratio Solution

Edge Length of Antiprism given Surface to Volume Ratio Formula Elements

Other Formulas to find Edge Length of Antiprism

How to Evaluate Edge Length of Antiprism given Surface to Volume Ratio?

FAQs on Edge Length of Antiprism given Surface to Volume Ratio

Variable Name

GoEdge Length of Antiprism Formula

GoEdge Length of Antiprism given Total Surface Area Formula