Edge Length of Antiprism given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Antiprism = ((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3)
le = ((12*(sin(pi/NVertices))^2*V)/(NVertices*sin((3*pi)/(2*NVertices))*sqrt(4*(cos(pi/(2*NVertices))^2)-1)))^(1/3)
This formula uses 1 Constants, 3 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Edge Length of Antiprism - (Measured in Meter) - Edge Length of Antiprism is defined as the straight line joining the adjacent vertices of the Antiprism.
Number of Vertices of Antiprism - Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.
Volume of Antiprism - (Measured in Cubic Meter) - Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.
STEP 1: Convert Input(s) to Base Unit
Number of Vertices of Antiprism: 5 --> No Conversion Required
Volume of Antiprism: 1580 Cubic Meter --> 1580 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
le = ((12*(sin(pi/NVertices))^2*V)/(NVertices*sin((3*pi)/(2*NVertices))*sqrt(4*(cos(pi/(2*NVertices))^2)-1)))^(1/3) --> ((12*(sin(pi/5))^2*1580)/(5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)))^(1/3)
Evaluating ... ...
le = 10.0027666655549
STEP 3: Convert Result to Output's Unit
10.0027666655549 Meter --> No Conversion Required
FINAL ANSWER
10.0027666655549 10.00277 Meter <-- Edge Length of Antiprism
(Calculation completed in 00.004 seconds)

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4 Edge Length of Antiprism Calculators

Edge Length of Antiprism given Surface to Volume Ratio
Go Edge Length of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Surface to Volume Ratio of Antiprism)
Edge Length of Antiprism given Volume
Go Edge Length of Antiprism = ((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3)
Edge Length of Antiprism given Total Surface Area
Go Edge Length of Antiprism = sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))))
Edge Length of Antiprism
Go Edge Length of Antiprism = Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))

Edge Length of Antiprism given Volume Formula

Edge Length of Antiprism = ((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3)
le = ((12*(sin(pi/NVertices))^2*V)/(NVertices*sin((3*pi)/(2*NVertices))*sqrt(4*(cos(pi/(2*NVertices))^2)-1)))^(1/3)

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 Volume?

Edge Length of Antiprism given Volume calculator uses Edge Length of Antiprism = ((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3) to calculate the Edge Length of Antiprism, The Edge Length of Antiprism given Volume formula is defined as the straight line joining two adjacent vertices of Antiprism and calculated using the volume of Antiprism. Edge Length of Antiprism is denoted by le symbol.

How to calculate Edge Length of Antiprism given Volume using this online calculator? To use this online calculator for Edge Length of Antiprism given Volume, enter Number of Vertices of Antiprism (NVertices) & Volume of Antiprism (V) and hit the calculate button. Here is how the Edge Length of Antiprism given Volume calculation can be explained with given input values -> 10.00277 = ((12*(sin(pi/5))^2*1580)/(5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)))^(1/3).

FAQ

What is Edge Length of Antiprism given Volume?
The Edge Length of Antiprism given Volume formula is defined as the straight line joining two adjacent vertices of Antiprism and calculated using the volume of Antiprism and is represented as le = ((12*(sin(pi/NVertices))^2*V)/(NVertices*sin((3*pi)/(2*NVertices))*sqrt(4*(cos(pi/(2*NVertices))^2)-1)))^(1/3) or Edge Length of Antiprism = ((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3). Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism & Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.
How to calculate Edge Length of Antiprism given Volume?
The Edge Length of Antiprism given Volume formula is defined as the straight line joining two adjacent vertices of Antiprism and calculated using the volume of Antiprism is calculated using Edge Length of Antiprism = ((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3). To calculate Edge Length of Antiprism given Volume, you need Number of Vertices of Antiprism (NVertices) & Volume of Antiprism (V). With our tool, you need to enter the respective value for Number of Vertices of Antiprism & Volume of Antiprism 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 Edge Length of Antiprism?
In this formula, Edge Length of Antiprism uses Number of Vertices of Antiprism & Volume of Antiprism. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Edge Length of Antiprism = Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))
  • Edge Length of Antiprism = sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))))
  • Edge Length of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Surface to Volume Ratio of Antiprism)
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