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## Volume of Antiprism given surface area 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)))*((sqrt(Area/((Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))))^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((sqrt(A/((n/2)*(cot(pi/n)+sqrt(3)))))^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.
Area - The area is the amount of two-dimensional space taken up by an object. (Measured in Square Meter)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
Area: 50 Square Meter --> 50 Square 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)))*((sqrt(A/((n/2)*(cot(pi/n)+sqrt(3)))))^3))/(12*(sin(pi/n))^2) --> (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*((sqrt(50/((1/2)*(cot(pi/1)+sqrt(3)))))^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 00.016 seconds)

## < 11 Other formulas that you can solve using the same Inputs

Diagonal of a Rectangle when breadth and area are given
diagonal = sqrt(((Area)^2/(Breadth)^2)+(Breadth)^2) Go
Diagonal of a Rectangle when length and area are given
diagonal = sqrt(((Area)^2/(Length)^2)+(Length)^2) Go
Side of a Kite when other side and area are given
side_a = (Area*cosec(Angle Between Sides))/Side B Go
Perimeter of rectangle when area and rectangle length are given
perimeter = (2*Area+2*(Length)^2)/Length Go
Buoyant Force
buoyant_force = Pressure*Area Go
Perimeter of a square when area is given
perimeter = 4*sqrt(Area) Go
Diagonal of a Square when area is given
diagonal = sqrt(2*Area) Go
Length of rectangle when area and breadth are given
length = Area/Breadth Go
Breadth of rectangle when area and length are given
breadth = Area/Length Go
Pressure when force and area are given
pressure = Force/Area Go
Stress
stress = Force/Area 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 given surface area Formula

volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((sqrt(Area/((Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))))^3))/(12*(sin(pi/Number Of Vertices))^2)
V = (n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*((sqrt(A/((n/2)*(cot(pi/n)+sqrt(3)))))^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 area?

Volume of Antiprism given surface area calculator uses volume = (Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices)))*((sqrt(Area/((Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))))^3))/(12*(sin(pi/Number Of Vertices))^2) to calculate the Volume, The Volume of Antiprism given surface area 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 area using this online calculator? To use this online calculator for Volume of Antiprism given surface area, enter Number Of Vertices (n) and Area (A) and hit the calculate button. Here is how the Volume of Antiprism given surface area calculation can be explained with given input values -> NaN = (1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*((sqrt(50/((1/2)*(cot(pi/1)+sqrt(3)))))^3))/(12*(sin(pi/1))^2).

### FAQ

What is Volume of Antiprism given surface area?
The Volume of Antiprism given surface area 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)))*((sqrt(A/((n/2)*(cot(pi/n)+sqrt(3)))))^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)))*((sqrt(Area/((Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))))^3))/(12*(sin(pi/Number Of Vertices))^2). Number Of Vertices is the number of vertices in the given two dimensional figure and The area is the amount of two-dimensional space taken up by an object.
How to calculate Volume of Antiprism given surface area?
The Volume of Antiprism given surface area 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)))*((sqrt(Area/((Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3)))))^3))/(12*(sin(pi/Number Of Vertices))^2). To calculate Volume of Antiprism given surface area, you need Number Of Vertices (n) and Area (A). With our tool, you need to enter the respective value for Number Of Vertices and Area 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 Area. 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
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