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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/NVertices))^2)*(NVertices/2)*(cot(pi/NVertices)+sqrt(3)))/((NVertices*sqrt(4*(cos(pi/(2*NVertices))^2)-1)*(sin((3*pi)/(2*NVertices)))*RAV))
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 three 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: 5 --> 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/NVertices))^2)*(NVertices/2)*(cot(pi/NVertices)+sqrt(3)))/((NVertices*sqrt(4*(cos(pi/(2*NVertices))^2)-1)*(sin((3*pi)/(2*NVertices)))*RAV)) --> ((12*(sin(pi/5))^2)*(5/2)*(cot(pi/5)+sqrt(3)))/((5*sqrt(4*(cos(pi/(2*5))^2)-1)*(sin((3*pi)/(2*5)))*0.5))
Evaluating ... ...
S = 9.84497924060948
STEP 3: Convert Result to Output's Unit
9.84497924060948 Meter --> No Conversion Required
FINAL ANSWER
9.84497924060948 Meter <-- Side
(Calculation completed in 00.000 seconds)

4 Edge length of Antiprism Calculators

Edge length of Antiprism given surface to volume ratio
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)) Go
Edge length of Antiprism given volume
side = (((12*sin(pi/Number of Vertices))*Volume)/((Number of Vertices*sqrt(4*(cos(pi/(2*Number of Vertices))^2)-1)*(sin((3*pi)/(2*Number of Vertices))))))^(1/3) Go
Edge length of Antiprism given surface area
side = sqrt(Surface Area/((Number of Vertices/2)*(cot(pi/Number of Vertices)+sqrt(3)))) Go
Edge length of Antiprism given height
side = Height/(sqrt(1-((sec(pi/(2*Number of Vertices)))^2)/4)) 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/NVertices))^2)*(NVertices/2)*(cot(pi/NVertices)+sqrt(3)))/((NVertices*sqrt(4*(cos(pi/(2*NVertices))^2)-1)*(sin((3*pi)/(2*NVertices)))*RAV))

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 (NVertices) & Surface to Volume Ratio (RAV) 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 -> 9.844979 = ((12*(sin(pi/5))^2)*(5/2)*(cot(pi/5)+sqrt(3)))/((5*sqrt(4*(cos(pi/(2*5))^2)-1)*(sin((3*pi)/(2*5)))*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/NVertices))^2)*(NVertices/2)*(cot(pi/NVertices)+sqrt(3)))/((NVertices*sqrt(4*(cos(pi/(2*NVertices))^2)-1)*(sin((3*pi)/(2*NVertices)))*RAV)) 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 three dimensional figure & 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 (NVertices) & Surface to Volume Ratio (RAV). With our tool, you need to enter the respective value for Number of Vertices & 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 & Surface to Volume Ratio. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • side = Height/(sqrt(1-((sec(pi/(2*Number of Vertices)))^2)/4))
  • side = sqrt(Surface Area/((Number of Vertices/2)*(cot(pi/Number of Vertices)+sqrt(3))))
  • side = (((12*sin(pi/Number of Vertices))*Volume)/((Number of Vertices*sqrt(4*(cos(pi/(2*Number of Vertices))^2)-1)*(sin((3*pi)/(2*Number of Vertices))))))^(1/3)
  • 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))
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