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Volume of Antiprism given Total Surface Area Formula

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Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism. Check FAQs

V = \frac{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} \cdot {(\sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2}}

V - Volume of Antiprism?N_Vertices - Number of Vertices of Antiprism?TSA - Total Surface Area of Antiprism?π - Archimedes' constant?

Volume of Antiprism given Total Surface Area Example

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Here is how the Volume of Antiprism given Total Surface Area equation looks like with Values.

Here is how the Volume of Antiprism given Total Surface Area equation looks like with Units.

Here is how the Volume of Antiprism given Total Surface Area equation looks like.

1587.5096 = \frac{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot {(\sqrt{\frac{780}{\frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

1587.5096m³ = \frac{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot {(\sqrt{\frac{780m²}{\frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

1587.5096 = \frac{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot {(\sqrt{\frac{780}{\frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

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Volume of Antiprism given Total Surface Area Solution

Follow our step by step solution on how to calculate Volume of Antiprism given Total Surface Area?

FIRST Step Consider the formula

V = \frac{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} \cdot {(\sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2}}

Next Step Substitute values of Variables

∴

V = \frac{5 \cdot \sin (\frac{3 \cdot π}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot 5})}^{2}) - 1} \cdot {(\sqrt{\frac{780m²}{\frac{5}{2} \cdot (\cot (\frac{π}{5}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{π}{5}))}^{2}}

Next Step Substitute values of Constants

∴

V = \frac{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot {(\sqrt{\frac{780m²}{\frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

Next Step Prepare to Evaluate

∴

V = \frac{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1} \cdot {(\sqrt{\frac{780}{\frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3})}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

Next Step Evaluate

∴

V = 1587.50957791706m³

LAST Step Rounding Answer

∴

V = 1587.5096m³

Volume of Antiprism given Total Surface Area Formula Elements

Variables

Constants

Functions

Volume of Antiprism

Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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

Total Surface Area of Antiprism

The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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 Volume of Antiprism

Go Volume of Antiprism

V = \frac{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} \cdot {l e}^{3}}{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2}}

Go Volume of Antiprism given Height

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

Go Volume of Antiprism given Surface to Volume Ratio

V = \frac{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} \cdot {(\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})}^{3}}{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2}}

How to Evaluate Volume of Antiprism given Total Surface Area?

Volume of Antiprism given Total Surface Area evaluator uses 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2) to evaluate the Volume of Antiprism, The Volume of Antiprism given Total Surface Area formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism, calculated using the total surface area of Antiprism. Volume of Antiprism is denoted by V symbol.

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

FAQs on Volume of Antiprism given Total Surface Area

What is the formula to find Volume of Antiprism given Total Surface Area?

The formula of Volume of Antiprism given Total Surface Area is expressed as 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2). Here is an example- 1587.51 = (5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*(sqrt(780/(5/2*(cot(pi/5)+sqrt(3)))))^3)/(12*(sin(pi/5))^2).

How to calculate Volume of Antiprism given Total Surface Area?

With Number of Vertices of Antiprism (N_Vertices) & Total Surface Area of Antiprism (TSA) we can find Volume of Antiprism given Total Surface Area using the formula - 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2). This formula also uses Archimedes' constant and , Sine, Cosine, Cotangent, Square Root Function function(s).

What are the other ways to Calculate Volume of Antiprism?

Here are the different ways to Calculate Volume of Antiprism-

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)*Edge Length of Antiprism^3)/(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)*(Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))^3)/(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)*((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))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)

Can the Volume of Antiprism given Total Surface Area be negative?

No, the Volume of Antiprism given Total Surface Area, measured in Volume cannot be negative.

Which unit is used to measure Volume of Antiprism given Total Surface Area?

Volume of Antiprism given Total Surface Area is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Antiprism given Total Surface Area can be measured.

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Volume of Antiprism given Total Surface Area Formula

​GoVolume of Antiprism Formula

​GoVolume of Antiprism given Height Formula

Volume of Antiprism given Total Surface Area Example

Volume of Antiprism given Total Surface Area Solution

Volume of Antiprism given Total Surface Area Formula Elements

Other Formulas to find Volume of Antiprism

How to Evaluate Volume of Antiprism given Total Surface Area?

FAQs on Volume of Antiprism given Total Surface Area

Variable Name

GoVolume of Antiprism Formula

GoVolume of Antiprism given Height Formula