Credits

St Joseph's College (St Joseph's College), Bengaluru
Mona Gladys has created this Calculator and 1000+ more calculators!
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 500+ more calculators!

Volume of Antiprism 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)))*(Side^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*(s^3))/(12*(sin(pi/n))^2)
This formula uses 1 Constants, 3 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(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.
Side - The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
Side: 9 Meter --> 9 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)))*(s^3))/(12*(sin(pi/n))^2) --> (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*(9^3))/(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)

11 Other formulas that you can solve using the same Inputs

Total Surface Area of a Pyramid
total_surface_area = Side*(Side+sqrt(Side^2+4*(Height)^2)) Go
Area of a Rhombus when side and diagonals are given
area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2)) Go
Lateral Surface Area of a Pyramid
lateral_surface_area = Side*sqrt(Side^2+4*(Height)^2) Go
Surface Area of a Capsule
surface_area = 2*pi*Radius*(2*Radius+Side) Go
Volume of a Capsule
volume = pi*(Radius)^2*((4/3)*Radius+Side) Go
Area of a Octagon
area = 2*(1+sqrt(2))*(Side)^2 Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Hexagon
area = (3/2)*sqrt(3)*Side^2 Go
Base Surface Area of a Pyramid
base_surface_area = Side^2 Go
Surface Area of a Cube
surface_area = 6*Side^2 Go
Volume of a Cube
volume = Side^3 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 Formula

volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*(Side^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*(s^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?

Volume of Antiprism calculator uses volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*(Side^3))/(12*(sin(pi/Number Of Vertices))^2) to calculate the Volume, The Volume of Antiprism 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 using this online calculator? To use this online calculator for Volume of Antiprism, enter Number Of Vertices (n) and Side (s) and hit the calculate button. Here is how the Volume of Antiprism calculation can be explained with given input values -> NaN = (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*(9^3))/(12*(sin(pi/1))^2).

FAQ

What is Volume of Antiprism?
The Volume of Antiprism 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)))*(s^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)))*(Side^3))/(12*(sin(pi/Number Of Vertices))^2). Number Of Vertices is the number of vertices in the given two dimensional figure and The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Volume of Antiprism?
The Volume of Antiprism 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)))*(Side^3))/(12*(sin(pi/Number Of Vertices))^2). To calculate Volume of Antiprism, you need Number Of Vertices (n) and Side (s). With our tool, you need to enter the respective value for Number Of Vertices and Side 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 Side. 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
Share Image
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!