Height of Antiprism given Volume Calculator

✖Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.ⓘ Number of Vertices of Antiprism [N_Vertices]			+10% -10%
✖Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.ⓘ Volume of Antiprism [V]			+10% -10%

✖Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.ⓘ Height of Antiprism given Volume [h]

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Formula

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Height of Antiprism given Volume

Formula

`"h" = sqrt(1-((sec(pi/(2*"N"_{"Vertices"})))^2)/4)*((12*(sin(pi/"N"_{"Vertices"}))^2*"V")/("N"_{"Vertices"}*sin((3*pi)/(2*"N"_{"Vertices"}))*sqrt(4*(cos(pi/(2*"N"_{"Vertices"}))^2)-1)))^(1/3)`

Example

`"8.508862m"=sqrt(1-((sec(pi/(2*"5")))^2)/4)*((12*(sin(pi/"5"))^2*"1580m³")/("5"*sin((3*pi)/(2*"5"))*sqrt(4*(cos(pi/(2*"5"))^2)-1)))^(1/3)`

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Height of Antiprism given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
h = sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)*((12*(sin(pi/N_Vertices))^2*V)/(N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)))^(1/3)
This formula uses 1 Constants, 4 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., 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., sqrt(Number)

Variables Used

Height of Antiprism - (Measured in Meter) - Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.
Number of Vertices of Antiprism - Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.
Volume of Antiprism - (Measured in Cubic Meter) - Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.

STEP 1: Convert Input(s) to Base Unit

Number of Vertices of Antiprism: 5 --> No Conversion Required
Volume of Antiprism: 1580 Cubic Meter --> 1580 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)*((12*(sin(pi/N_Vertices))^2*V)/(N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)))^(1/3) --> 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)

Evaluating ... ...

h = 8.50886154981112

STEP 3: Convert Result to Output's Unit

8.50886154981112 Meter --> No Conversion Required

FINAL ANSWER

8.50886154981112 ≈ 8.508862 Meter <-- Height of Antiprism

(Calculation completed in 00.020 seconds)

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St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< 4 Height of Antiprism Calculators

Height of Antiprism given Surface to Volume Ratio

Go 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)

Height of Antiprism given Volume

Go 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)

Height of Antiprism given Total Surface Area

Go 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

Go Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*Edge Length of Antiprism

Height of Antiprism given Volume Formula

What is an Antiprism?

In geometry, an n-gonal antiprism or n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles. Antiprisms are a subclass of prismatoids and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms except that the bases are twisted relatively to each other, and that the side faces are triangles, rather than quadrilaterals. In the case of a regular n-sided base, one usually considers the case where its copy is twisted by an angle of 180/n degrees. Extra regularity is obtained when the line connecting the base centers is perpendicular to the base planes, making it a right antiprism. As faces, it has the two n-gonal bases and, connecting those bases, 2n isosceles triangles.

How to Calculate Height of Antiprism given Volume?

Height of Antiprism given Volume calculator 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 calculate 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 calculate Height of Antiprism given Volume using this online calculator? To use this online calculator for Height of Antiprism given Volume, enter Number of Vertices of Antiprism (N_Vertices) & Volume of Antiprism (V) and hit the calculate button. Here is how the Height of Antiprism given Volume calculation can be explained with given input values -> 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).

FAQ

What is Height of Antiprism given Volume?

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 and is represented as h = sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)*((12*(sin(pi/N_Vertices))^2*V)/(N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)))^(1/3) or 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). Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism & Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.

How to calculate Height of Antiprism given Volume?

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 is calculated using 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 calculate Height of Antiprism given Volume, you need Number of Vertices of Antiprism (N_Vertices) & Volume of Antiprism (V). With our tool, you need to enter the respective value for Number of Vertices of Antiprism & Volume of Antiprism and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Height of Antiprism?

In this formula, Height of Antiprism uses Number of Vertices of Antiprism & Volume of Antiprism. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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