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## Volume of Antiprism given height Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((h/(sqrt(1-((sec(pi/(2*n)))^2)/4)))^3))/(12*(sin(pi/n))^2)
This formula uses 2 Constants, 4 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sin - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(Angle)
sec - Trigonometric secant function, sec(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Number Of Vertices- Number Of Vertices is the number of vertices in the given two dimensional figure.
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
Height: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((h/(sqrt(1-((sec(pi/(2*n)))^2)/4)))^3))/(12*(sin(pi/n))^2) --> (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*((12/(sqrt(1-((sec(pi/(2*1)))^2)/4)))^3))/(12*(sin(pi/1))^2)
Evaluating ... ...
V = NaN
STEP 3: Convert Result to Output's Unit
NaN Cubic Meter --> No Conversion Required
NaN Cubic Meter <-- Volume
(Calculation completed in 00.031 seconds)

## < 11 Other formulas that you can solve using the same Inputs

Volume of a Conical Frustum
Total Surface Area of a Cone
Lateral Surface Area of a Cone
Total Surface Area of a Cylinder
Lateral Surface Area of a Cylinder
Volume of a Circular Cone
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Parallelogram when base and height are given
area = Base*Height Go

## < 11 Other formulas that calculate the same Output

Volume of a Conical Frustum
Volume of a Capsule
Volume of a Circular Cone
Volume of a Circular Cylinder
Volume of a Rectangular Prism
volume = Width*Height*Length Go
Volume of Regular Dodecahedron
volume = ((15+(7*sqrt(5)))*Side^3)/4 Go
Volume of Regular Icosahedron
volume = (5*(3+sqrt(5))*Side^3)/12 Go
Volume of a Hemisphere
Volume of a Sphere
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Volume of a Cube
volume = Side^3 Go

### Volume of Antiprism given height Formula

volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((h/(sqrt(1-((sec(pi/(2*n)))^2)/4)))^3))/(12*(sin(pi/n))^2)

## 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 = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))^3))/(12*(sin(pi/Number Of Vertices))^2) to calculate the Volume, The Volume of Antiprism given height formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of Antiprism. Volume and 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 (n) and Height (h) and hit the calculate button. Here is how the Volume of Antiprism given height calculation can be explained with given input values -> NaN = (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*((12/(sqrt(1-((sec(pi/(2*1)))^2)/4)))^3))/(12*(sin(pi/1))^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 where a = edge length of Antiprism and is represented as V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((h/(sqrt(1-((sec(pi/(2*n)))^2)/4)))^3))/(12*(sin(pi/n))^2) or volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))^3))/(12*(sin(pi/Number Of Vertices))^2). Number Of Vertices is the number of vertices in the given two dimensional figure and Height is the distance between the lowest and highest points of a person standing upright.
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 where a = edge length of Antiprism is calculated using volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))^3))/(12*(sin(pi/Number Of Vertices))^2). To calculate Volume of Antiprism given height, you need Number Of Vertices (n) and Height (h). With our tool, you need to enter the respective value for Number Of Vertices and Height 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?
In this formula, Volume uses Number Of Vertices and Height. We can use 11 other way(s) to calculate the same, which is/are as follows -