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Height of Antiprism given Volume Formula

GoHeight of Antiprism Formula

GoHeight of Antiprism given Total Surface Area Formula

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

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

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

Height of Antiprism given Volume Example

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

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

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

8.5089 = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{1}{3}}

8.5089m = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580m³}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{1}{3}}

8.5089 = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{1}{3}}

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Height of Antiprism given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot 5}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{π}{5}))}^{2} \cdot 1580m³}{5 \cdot \sin (\frac{3 \cdot π}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot 5})}^{2}) - 1}})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

h = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580m³}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

h = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{1}{3}}

Next Step Evaluate

∴

h = 8.50886154981112m

LAST Step Rounding Answer

∴

h = 8.5089m

Height of Antiprism given Volume Formula Elements

Variables

Constants

Functions

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

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

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

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 Height of Antiprism

Go Height of Antiprism

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

Go Height of Antiprism given Total Surface Area

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}} \cdot \sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}}

Go Height of Antiprism given Surface to Volume Ratio

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

How to Evaluate Height of Antiprism given Volume?

Height of Antiprism given Volume evaluator uses Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*((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) to evaluate the Height of Antiprism, The Height of Antiprism given Volume formula is defined as the measure of vertical distance from one top to bottom face of Antiprism, calculated using the volume of Antiprism. Height of Antiprism is denoted by h symbol.

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

FAQs on Height of Antiprism given Volume

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

The formula of Height of Antiprism given Volume is expressed as Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*((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). Here is an example- 8.508862 = sqrt(1-((sec(pi/(2*5)))^2)/4)*((12*(sin(pi/5))^2*1580)/(5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)))^(1/3).

How to calculate Height of Antiprism given Volume?

With Number of Vertices of Antiprism (N_Vertices) & Volume of Antiprism (V) we can find Height of Antiprism given Volume using the formula - Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*((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). 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 Height of Antiprism?

Here are the different ways to Calculate Height of Antiprism-

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

Can the Height of Antiprism given Volume be negative?

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

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

Height of Antiprism given Volume is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Antiprism given Volume can be measured.

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Height of Antiprism given Volume Formula

​GoHeight of Antiprism Formula

​GoHeight of Antiprism given Total Surface Area Formula

Height of Antiprism given Volume Example

Height of Antiprism given Volume Solution

Height of Antiprism given Volume Formula Elements

Other Formulas to find Height of Antiprism

How to Evaluate Height of Antiprism given Volume?

FAQs on Height of Antiprism given Volume

Variable Name

GoHeight of Antiprism Formula

GoHeight of Antiprism given Total Surface Area Formula