Volume of Antiprism given height Calculator

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3D Geometry	Antiprism ↺

✖Number Of Vertices is the number of vertices in the given two dimensional figure.ⓘ Number Of Vertices [n]			+10% -10%
✖Height is the distance between the lowest and highest points of a person standing upright.ⓘ Height [h]			+10% -10%

✖Volume is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume of Antiprism given height [V]

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Credits

Mona Gladys

St Joseph's College (St Joseph's College), Bengaluru

Mona Gladys has created this Calculator and 1000+ more calculators!

Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 500+ more calculators!

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

FINAL ANSWER

NaN Cubic Meter <-- Volume

(Calculation completed in 00.031 seconds)

You are here

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

Volume of a Conical Frustum

volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go

Total Surface Area of a Cone

total_surface_area = pi*Radius*(Radius+sqrt(Radius^2+Height^2)) Go

Lateral Surface Area of a Cone

lateral_surface_area = pi*Radius*sqrt(Radius^2+Height^2) Go

Total Surface Area of a Cylinder

total_surface_area = 2*pi*Radius*(Height+Radius) Go

Lateral Surface Area of a Cylinder

lateral_surface_area = 2*pi*Radius*Height Go

Volume of a Circular Cone

volume = (1/3)*pi*(Radius)^2*Height Go

Area of a Trapezoid

area = ((Base A+Base B)/2)*Height Go

Volume of a Circular Cylinder

volume = pi*(Radius)^2*Height Go

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 = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go

Volume of a Capsule

volume = pi*(Radius)^2*((4/3)*Radius+Side) Go

Volume of a Circular Cone

volume = (1/3)*pi*(Radius)^2*Height Go

Volume of a Circular Cylinder

volume = pi*(Radius)^2*Height Go

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 = (2/3)*pi*(Radius)^3 Go

Volume of a Sphere

volume = (4/3)*pi*(Radius)^3 Go

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

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 -

volume = pi*(Radius)^2*((4/3)*Radius+Side)
volume = (1/3)*pi*(Radius)^2*Height
volume = pi*(Radius)^2*Height
volume = Side^3
volume = (2/3)*pi*(Radius)^3
volume = (4/3)*pi*(Radius)^3
volume = (1/3)*Side^2*Height
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2))
volume = Width*Height*Length
volume = ((15+(7*sqrt(5)))*Side^3)/4
volume = (5*(3+sqrt(5))*Side^3)/12

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