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## Surface area of Antiprism given volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*(((((12*(sin(pi/Number Of Vertices))^2)*Volume)/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices))))))^(1/3))^2)
SA = (n/2)*(cot(pi/n)+sqrt(3))*(((((12*(sin(pi/n))^2)*V)/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n))))))^(1/3))^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.
Volume - Volume is the amount of space that a substance or object occupies or that is enclosed within a container. (Measured in Cubic Meter)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
SA = (n/2)*(cot(pi/n)+sqrt(3))*(((((12*(sin(pi/n))^2)*V)/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n))))))^(1/3))^2) --> (1/2)*(cot(pi/1)+sqrt(3))*(((((12*(sin(pi/1))^2)*63)/((1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1))))))^(1/3))^2)
Evaluating ... ...
SA = NaN
STEP 3: Convert Result to Output's Unit
NaN Square Meter --> No Conversion Required
NaN Square Meter <-- Surface Area
(Calculation completed in 00.031 seconds)

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

Slant height of a Right square pyramid when volume and side length are given
slant_height = sqrt((Side^2/4)+((3*Volume)/Side^2)^2) Go
Lateral edge length of a Right square pyramid when volume and side length is given
length_edge = sqrt(Side^2/2+((3*Volume)/Side^2)^2) Go
Specific Weight
specific_weight = Weight of body on which frictional force is applied/Volume Go
Height of a triangular prism when base and volume are given
height = (2*Volume)/(Base*Length) Go
Side length of a Right square pyramid when volume and height are given
side = sqrt((3*Volume)/Height) Go
Bottom surface area of a triangular prism when volume and height are given
bottom_surface_area = Volume/Height Go
Body Force Work Rate
body_force_work_rate = Force/Volume Go
Top surface area of a triangular prism when volume and height are given
top_surface_area = Volume/Height Go
Specific Volume
specific_volume = Volume/Mass Go
Height of a right square pyramid when volume and side length are given
height = (3*Volume)/Side^2 Go
Density
density = Mass/Volume Go

## < 11 Other formulas that calculate the same Output

Surface Area of Cuboid
Surface Area of a Rectangular Prism
surface_area = 2*(Length*Width+Length*Height+Width*Height) Go
Surface Area of triangular prism
surface_area = (Base*Height)+(2*Length*Side)+(Length*Base) Go
Surface Area of a Capsule
Surface Area of Prisms
surface_area = (2*Base Area)+(Height*Base Perimeter) Go
Surface Area of Dodecahedron
surface_area = 3*(sqrt(25+(10*sqrt(5))))*(Side^2) Go
Surface Area of Regular Octahedron
surface_area = 2*(sqrt(3))*(Side^2) Go
Surface Area of Icosahedron
surface_area = 5*(sqrt(3))*(Side^2) Go
Surface Area of Regular Tetrahedron
surface_area = (sqrt(3))*(Side^2) Go
Surface Area of a Sphere
Surface Area of a Cube
surface_area = 6*Side^2 Go

### Surface area of Antiprism given volume Formula

surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*(((((12*(sin(pi/Number Of Vertices))^2)*Volume)/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices))))))^(1/3))^2)
SA = (n/2)*(cot(pi/n)+sqrt(3))*(((((12*(sin(pi/n))^2)*V)/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n))))))^(1/3))^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 Surface area of Antiprism given volume?

Surface area of Antiprism given volume calculator uses surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*(((((12*(sin(pi/Number Of Vertices))^2)*Volume)/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices))))))^(1/3))^2) to calculate the Surface Area, The Surface area of Antiprism given volume formula is defined as measure of the total area that the surface of the object occupies of a Antiprism, where a =Antiprism edge. Surface Area and is denoted by SA symbol.

How to calculate Surface area of Antiprism given volume using this online calculator? To use this online calculator for Surface area of Antiprism given volume, enter Number Of Vertices (n) and Volume (V) and hit the calculate button. Here is how the Surface area of Antiprism given volume calculation can be explained with given input values -> NaN = (1/2)*(cot(pi/1)+sqrt(3))*(((((12*(sin(pi/1))^2)*63)/((1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1))))))^(1/3))^2).

### FAQ

What is Surface area of Antiprism given volume?
The Surface area of Antiprism given volume formula is defined as measure of the total area that the surface of the object occupies of a Antiprism, where a =Antiprism edge and is represented as SA = (n/2)*(cot(pi/n)+sqrt(3))*(((((12*(sin(pi/n))^2)*V)/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n))))))^(1/3))^2) or surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*(((((12*(sin(pi/Number Of Vertices))^2)*Volume)/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices))))))^(1/3))^2). Number Of Vertices is the number of vertices in the given two dimensional figure and Volume is the amount of space that a substance or object occupies or that is enclosed within a container.
How to calculate Surface area of Antiprism given volume?
The Surface area of Antiprism given volume formula is defined as measure of the total area that the surface of the object occupies of a Antiprism, where a =Antiprism edge is calculated using surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*(((((12*(sin(pi/Number Of Vertices))^2)*Volume)/((Number Of Vertices*sqrt(4*(cos(pi/(2*Number Of Vertices))^2)-1)*(sin((3*pi)/(2*Number Of Vertices))))))^(1/3))^2). To calculate Surface area of Antiprism given volume, you need Number Of Vertices (n) and Volume (V). With our tool, you need to enter the respective value for Number Of Vertices and Volume 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 Surface Area?
In this formula, Surface Area uses Number Of Vertices and Volume. We can use 11 other way(s) to calculate the same, which is/are as follows -
• surface_area = 6*Side^2
• surface_area = 2*(Length*Width+Length*Height+Width*Height)