Volume of Antiprism given Height 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%
✖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 [h]			+10% -10%

✖Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.ⓘ Volume of Antiprism given Height [V]

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Volume of Antiprism given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Number of Vertices of Antiprism - Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.
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.

STEP 1: Convert Input(s) to Base Unit

Number of Vertices of Antiprism: 5 --> No Conversion Required
Height of Antiprism: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

V = 1313.14497586144

STEP 3: Convert Result to Output's Unit

1313.14497586144 Cubic Meter --> No Conversion Required

FINAL ANSWER

1313.14497586144 ≈ 1313.145 Cubic Meter <-- Volume of Antiprism

(Calculation completed in 00.004 seconds)

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< Volume of Antiprism Calculators

Volume of Antiprism given Surface to Volume Ratio

LaTeX Go 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)

Volume of Antiprism given Total Surface Area

LaTeX Go 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 given Height

Volume of Antiprism

Volume of Antiprism given Height Formula

LaTeX Go

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 Volume of Antiprism given Height?

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

FAQ

What is Volume of Antiprism given Height?

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 and is represented as V = (N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*(h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)))^3)/(12*(sin(pi/N_Vertices))^2) or 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). Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism & Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

How to calculate Volume of Antiprism given Height?

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 is calculated using 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 calculate Volume of Antiprism given Height, you need Number of Vertices of Antiprism (N_Vertices) & Height of Antiprism (h). With our tool, you need to enter the respective value for Number of Vertices of Antiprism & Height 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 Volume of Antiprism?

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

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)

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