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Volume of Antiprism given Height Formula

GoVolume of Antiprism Formula

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

V - Volume of Antiprism?N_Vertices - Number of Vertices of Antiprism?h - Height of Antiprism?π - Archimedes' constant?

Volume of Antiprism given Height Example

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

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

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

1313.145 = \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 {(\frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

1313.145m³ = \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 {(\frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

1313.145 = \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 {(\frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

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Volume of Antiprism given Height Solution

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

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 {(\frac{h}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}}})}^{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 {(\frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot 5}))}^{2}}{4}}})}^{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 {(\frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{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 {(\frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{3}}{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2}}

Next Step Evaluate

∴

V = 1313.14497586144m³

LAST Step Rounding Answer

∴

V = 1313.145m³

Volume of Antiprism given Height 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

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)

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 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 Total Surface Area

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}}

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 Height?

Volume of Antiprism given Height 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)*(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) to evaluate the Volume of Antiprism, The Volume of Antiprism given Height formula is defined as the quantity of three-dimensional space enclosed by a closed surface of an Antiprism, calculated using the height of Antiprism. Volume of Antiprism is denoted by V symbol.

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

FAQs on Volume of Antiprism given Height

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

The formula of Volume of Antiprism given Height 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)*(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). Here is an example- 1313.145 = (5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*(8/(sqrt(1-((sec(pi/(2*5)))^2)/4)))^3)/(12*(sin(pi/5))^2).

How to calculate Volume of Antiprism given Height?

With Number of Vertices of Antiprism (N_Vertices) & Height of Antiprism (h) we can find Volume of Antiprism given Height 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)*(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). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Secant (sec), Square Root (sqrt) 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)*(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)
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 Height be negative?

No, the Volume of Antiprism given Height, measured in Volume cannot be negative.

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

Volume of Antiprism given Height 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 Height can be measured.

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Volume of Antiprism given Height Formula

​GoVolume of Antiprism Formula

​GoVolume of Antiprism given Total Surface Area Formula

Volume of Antiprism given Height Example

Volume of Antiprism given Height Solution

Volume of Antiprism given Height Formula Elements

Other Formulas to find Volume of Antiprism

How to Evaluate Volume of Antiprism given Height?

FAQs on Volume of Antiprism given Height

Variable Name

GoVolume of Antiprism Formula

GoVolume of Antiprism given Total Surface Area Formula