Volume of Antiprism given surface area Calculator

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3D Geometry	Antiprism ↺

✖Number Of Vertices is the number of vertices in the given two dimensional figure.ⓘ Number Of Vertices [n]			+10% -10%
✖The area is the amount of two-dimensional space taken up by an object.ⓘ Area [A]			+10% -10%

✖Volume is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume of Antiprism given surface area [V]

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Credits

Mona Gladys

St Joseph's College (St Joseph's College), Bengaluru

Mona Gladys has created this Calculator and 1000+ more calculators!

Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 500+ more calculators!

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)

You are here

< 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

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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