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## Edge length of Antiprism given surface-to-volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
side = ((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))
s = ((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))
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
s = ((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)) --> ((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))
Evaluating ... ...
s = NaN
STEP 3: Convert Result to Output's Unit
NaN Meter --> No Conversion Required
NaN Meter <-- Side
(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

Side of a regular polygon when area is given
side = sqrt(4*Area of regular polygon*tan((180*pi/180)/Number of sides))/sqrt(Number of sides) Go
Side of a parallelogram when diagonal and the angle between diagonals are given
side = sqrt((Diagonal 1)^2+(Diagonal 2)^2-(2*Diagonal 1*Diagonal 2*Angle Between Two Diagonals))/2 Go
Side of a parallelogram when diagonal and the angle between diagonals are given
side = sqrt((Diagonal A)^2+(Diagonal B)^2+(2*Diagonal A*Diagonal B*Angle Between Two Diagonals))/2 Go
Side of a rhombus when diagonal and angle are given
side = Diagonal/sqrt(2+2*cos(Half angle between sides)) Go
Side of a rhombus when diagonal and half-angle are given
side = Diagonal/(2*cos(Angle Between Sides)) Go
Side of a Rhombus when diagonals are given
side = sqrt(Diagonal 1^2+Diagonal 2^2)/2 Go
Side length of a Right square pyramid when volume and height are given
side = sqrt((3*Volume)/Height) Go
Side of a regular polygon when perimeter is given
side = Perimeter of Regular Polygon/Number of sides Go
Side of a rhombus when area and inradius are given
Side of a rhombus when perimeter is given
side = Perimeter/4 Go
Side of Largest Cube that can be inscribed within a right circular cylinder of height h
side = Height Go

### Edge length of Antiprism given surface-to-volume ratio Formula

side = ((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))
s = ((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))

## 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 Edge length of Antiprism given surface-to-volume ratio?

Edge length of Antiprism given surface-to-volume ratio calculator uses side = ((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)) to calculate the Side, The Edge length of Antiprism given surface-to-volume ratio formula is defined as a straight line joining two adjacent vertices of Antiprism. Where, a = Antiprism edge. Side and is denoted by s symbol.

How to calculate Edge length of Antiprism given surface-to-volume ratio using this online calculator? To use this online calculator for Edge length 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 Edge length of Antiprism given surface-to-volume ratio calculation can be explained with given input values -> NaN = ((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)).

### FAQ

What is Edge length of Antiprism given surface-to-volume ratio?
The Edge length of Antiprism given surface-to-volume ratio formula is defined as a straight line joining two adjacent vertices of Antiprism. Where, a = Antiprism edge and is represented as s = ((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)) or side = ((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)). 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 Edge length of Antiprism given surface-to-volume ratio?
The Edge length of Antiprism given surface-to-volume ratio formula is defined as a straight line joining two adjacent vertices of Antiprism. Where, a = Antiprism edge is calculated using side = ((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)). To calculate Edge length 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 Side?
In this formula, Side 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 -
• side = Height
• side = sqrt(Diagonal 1^2+Diagonal 2^2)/2
• side = Perimeter/4
• side = Diagonal/sqrt(2+2*cos(Half angle between sides))
• side = Diagonal/(2*cos(Angle Between Sides))
• side = sqrt((Diagonal 1)^2+(Diagonal 2)^2-(2*Diagonal 1*Diagonal 2*Angle Between Two Diagonals))/2
• side = sqrt((Diagonal A)^2+(Diagonal B)^2+(2*Diagonal A*Diagonal B*Angle Between Two Diagonals))/2
• side = Perimeter of Regular Polygon/Number of sides
• side = sqrt(4*Area of regular polygon*tan((180*pi/180)/Number of sides))/sqrt(Number of sides)
• side = sqrt((3*Volume)/Height)
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