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Surface to Volume Ratio of Antiprism given Height Formula

GoSurface to Volume Ratio of Antiprism 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 \frac{h}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}}}}

R_A/V - Surface to Volume Ratio of Antiprism?N_Vertices - Number of Vertices of Antiprism?h - Height of Antiprism?π - Archimedes' constant?

Surface to Volume Ratio of Antiprism given Height Example

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

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

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

0.5234 = \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 \frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}}

0.5234m⁻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 \frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}}

0.5234 = \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 \frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}}

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Surface to Volume Ratio of Antiprism given Height Solution

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

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

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 \frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot 5}))}^{2}}{4}}}}

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 \frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}}

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 \frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}}

Next Step Evaluate

∴

R A/V = 0.523414971827094m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.5234m⁻¹

Surface to Volume Ratio of Antiprism given Height 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

Height of Antiprism

Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height 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)

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)

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

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}

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 given Height?

Surface to Volume Ratio of Antiprism given Height 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)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))) to evaluate the Surface to Volume Ratio of Antiprism, The Surface to Volume Ratio of Antiprism given Height formula is defined as the fraction of the surface area to the volume of Antiprism, calculated using the height of Antiprism. Surface to Volume Ratio of Antiprism is denoted by R_A/V symbol.

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

FAQs on Surface to Volume Ratio of Antiprism given Height

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

The formula of Surface to Volume Ratio of Antiprism given Height 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)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))). Here is an example- 0.523415 = (6*(sin(pi/5))^2*(cot(pi/5)+sqrt(3)))/(sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*8/(sqrt(1-((sec(pi/(2*5)))^2)/4))).

How to calculate Surface to Volume Ratio of Antiprism given Height?

With Number of Vertices of Antiprism (N_Vertices) & Height of Antiprism (h) we can find Surface to Volume Ratio of Antiprism given Height 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)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Cotangent (cot), Secant (sec), 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)*Edge Length 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)*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 given Height be negative?

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

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

Surface to Volume Ratio of Antiprism 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 Antiprism given Height can be measured.

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Surface to Volume Ratio of Antiprism given Height Formula

​GoSurface to Volume Ratio of Antiprism Formula

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

Surface to Volume Ratio of Antiprism given Height Example

Surface to Volume Ratio of Antiprism given Height Solution

Surface to Volume Ratio of Antiprism given Height Formula Elements

Other Formulas to find Surface to Volume Ratio of Antiprism

How to Evaluate Surface to Volume Ratio of Antiprism given Height?

FAQs on Surface to Volume Ratio of Antiprism given Height

Variable Name

GoSurface to Volume Ratio of Antiprism Formula

GoSurface to Volume Ratio of Antiprism given Total Surface Area Formula