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## Volume of Antiprism given surface-to-volume ratio 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)))*((((12*(sin(pi/Number Of Vertices))^2)*(Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*surface to volume ratio)))^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^3))/(12*(sin(pi/n))^2)
This formula uses 1 Constants, 4 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)
cot - Trigonometric cotangent function, cot(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.
surface to volume ratio - surface to volume ratio is fraction of surface to volume. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
surface to volume ratio: 0.5 Hundred --> 0.5 Hundred 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)))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^3))/(12*(sin(pi/n))^2) --> (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*((((12*(sin(pi/1))^2)*(1/2)*(cot(pi/1)+sqrt(3)))/((1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*0.5)))^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 triakis tetrahedron given surface-volume-ratio
volume = (3/20)*sqrt(2)*((4*sqrt(11))/(surface to volume ratio*sqrt(2)))^3 Go
side given Surface-to-volume ratio (A/V) of Rhombic Triacontahedron
side = (3*sqrt(5))/(surface to volume ratio*(sqrt(5+(2*sqrt(5))))) Go
height of triakis tetrahedron given surface-volime-ratio
height = (3/5)*(sqrt(6))*(4/surface to volume ratio)*(sqrt(11/2)) Go
edge length of Rhombic Dodecahedron given Surface-to-volume ratio
side_a = (9*sqrt(2))/(2*sqrt(3)*surface to volume ratio) Go
edge length of tetrahedron(a) of triakis tetrahedron given Surface-to-volume ratio (A/V)
side_a = (4*sqrt(11))/(surface to volume ratio*sqrt(2)) Go
Area of triakis tetrahedron given surface-volume-ratio
area = (3/5)*(sqrt(11/2))*(4/surface to volume ratio)^2 Go
Number Of Edges
no_of_edges = Number Of Faces +Number Of Vertices-2 Go
Value of E in Euler's formula
no_of_edges = Number of faces+Number Of Vertices-2 Go
Number Of Faces
no_of_faces = 2+Number Of Edges-Number Of Vertices Go
Midsphere radius of triakis tetrahedron given surface-volume-ratio
radius = sqrt(11)/surface to volume ratio Go
Insphere radius of triakis tetrahedron given surface-volume-ratio
radius = 3/surface to volume ratio 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 surface-to-volume ratio Formula

volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((((12*(sin(pi/Number Of Vertices))^2)*(Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*surface to volume ratio)))^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^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 surface-to-volume ratio?

Volume of Antiprism given surface-to-volume ratio calculator uses volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((((12*(sin(pi/Number Of Vertices))^2)*(Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*surface to volume ratio)))^3))/(12*(sin(pi/Number Of Vertices))^2) to calculate the Volume, The Volume of Antiprism given surface-to-volume ratio 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 surface-to-volume ratio using this online calculator? To use this online calculator for Volume of Antiprism given surface-to-volume ratio, enter Number Of Vertices (n) and surface to volume ratio (r) and hit the calculate button. Here is how the Volume of Antiprism given surface-to-volume ratio calculation can be explained with given input values -> NaN = (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*((((12*(sin(pi/1))^2)*(1/2)*(cot(pi/1)+sqrt(3)))/((1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*0.5)))^3))/(12*(sin(pi/1))^2).

### FAQ

What is Volume of Antiprism given surface-to-volume ratio?
The Volume of Antiprism given surface-to-volume ratio 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)))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^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)))*((((12*(sin(pi/Number Of Vertices))^2)*(Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*surface to volume ratio)))^3))/(12*(sin(pi/Number Of Vertices))^2). Number Of Vertices is the number of vertices in the given two dimensional figure and surface to volume ratio is fraction of surface to volume.
How to calculate Volume of Antiprism given surface-to-volume ratio?
The Volume of Antiprism given surface-to-volume ratio 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)))*((((12*(sin(pi/Number Of Vertices))^2)*(Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*surface to volume ratio)))^3))/(12*(sin(pi/Number Of Vertices))^2). To calculate Volume of Antiprism given surface-to-volume ratio, you need Number Of Vertices (n) and surface to volume ratio (r). With our tool, you need to enter the respective value for Number Of Vertices and surface to volume ratio 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 surface to volume ratio. We can use 11 other way(s) to calculate the same, which is/are as follows -