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Surface to Volume Ratio of Antiprism Formula

GoSurface to Volume Ratio of Antiprism given Height Formula

GoSurface to Volume Ratio of Antiprism given Total Surface Area Formula

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

R A/V = \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 l e}

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

Surface to Volume Ratio of Antiprism Example

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

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

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

0.4922 = \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 10}

0.4922m⁻¹ = \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 10m}

0.4922 = \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 10}

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Surface to Volume Ratio of Antiprism Solution

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

FIRST Step Consider the formula

R A/V = \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 l e}

Next Step Substitute values of Variables

∴

R A/V = \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 10m}

Next Step Substitute values of Constants

∴

R A/V = \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 10m}

Next Step Prepare to Evaluate

∴

R A/V = \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 10}

Next Step Evaluate

∴

R A/V = 0.492248962030474m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.4922m⁻¹

Surface to Volume Ratio of Antiprism Formula Elements

Variables

Constants

Functions

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

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

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

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 Surface to Volume Ratio of Antiprism

Go Surface to Volume Ratio of Antiprism given Height

R A/V = \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 \frac{h}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}}}}

Go Surface to Volume Ratio of Antiprism given Total Surface Area

R A/V = \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 \sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}}}

Go Surface to Volume Ratio of Antiprism given Volume

R A/V = \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 {(\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 Surface to Volume Ratio of Antiprism?

Surface to Volume Ratio of Antiprism evaluator uses Surface to Volume Ratio 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)*Edge Length of Antiprism) to evaluate the Surface to Volume Ratio of Antiprism, The Surface to Volume Ratio of Antiprism formula is defined as the fraction of the surface area to the volume of the Antiprism. Surface to Volume Ratio of Antiprism is denoted by R_A/V symbol.

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

FAQs on Surface to Volume Ratio of Antiprism

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

The formula of Surface to Volume Ratio of Antiprism is expressed as Surface to Volume Ratio 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)*Edge Length of Antiprism). Here is an example- 0.492249 = (6*(sin(pi/5))^2*(cot(pi/5)+sqrt(3)))/(sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*10).

How to calculate Surface to Volume Ratio of Antiprism?

With Number of Vertices of Antiprism (N_Vertices) & Edge Length of Antiprism (l_e) we can find Surface to Volume Ratio of Antiprism using the formula - Surface to Volume Ratio 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)*Edge Length 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 Surface to Volume Ratio of Antiprism?

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

Surface to Volume Ratio 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)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))
Surface to Volume Ratio 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)*sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))
Surface to Volume Ratio 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)*((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 Surface to Volume Ratio of Antiprism be negative?

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

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

Surface to Volume Ratio of Antiprism 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 Antiprism can be measured.

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Surface to Volume Ratio of Antiprism Formula

​GoSurface to Volume Ratio of Antiprism given Height Formula

​GoSurface to Volume Ratio of Antiprism given Total Surface Area Formula

Surface to Volume Ratio of Antiprism Example

Surface to Volume Ratio of Antiprism Solution

Surface to Volume Ratio of Antiprism Formula Elements

Other Formulas to find Surface to Volume Ratio of Antiprism

How to Evaluate Surface to Volume Ratio of Antiprism?

FAQs on Surface to Volume Ratio of Antiprism

Variable Name

GoSurface to Volume Ratio of Antiprism given Height Formula

GoSurface to Volume Ratio of Antiprism given Total Surface Area Formula