🔍
🔍

## Credits

St Joseph's College (St Joseph's College), Bengaluru
Mona Gladys has created this Calculator and 1000+ more calculators!
Walchand College of Engineering (WCE), Sangli
Shweta Patil has verified this Calculator and 500+ more calculators!

## Surface area of Antiprism given surface-to-volume ratio 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)*(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)))^2)
SA = (n/2)*(cot(pi/n)+sqrt(3))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^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.
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: 1 --> 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
SA = (n/2)*(cot(pi/n)+sqrt(3))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^2) --> (1/2)*(cot(pi/1)+sqrt(3))*((((12*(sin(pi/1))^2)*(1/2)*(cot(pi/1)+sqrt(3)))/((1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*0.5)))^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

Volume of triakis tetrahedron given surface-volume-ratio
volume = (3/20)*sqrt(2)*((4*sqrt(11))/(surface to volume ratio*sqrt(2)))^3 Go
side given Surface-to-volume ratio (A/V) of Rhombic Triacontahedron
side = (3*sqrt(5))/(surface to volume ratio*(sqrt(5+(2*sqrt(5))))) Go
height of triakis tetrahedron given surface-volime-ratio
height = (3/5)*(sqrt(6))*(4/surface to volume ratio)*(sqrt(11/2)) Go
edge length of Rhombic Dodecahedron given Surface-to-volume ratio
side_a = (9*sqrt(2))/(2*sqrt(3)*surface to volume ratio) Go
edge length of tetrahedron(a) of triakis tetrahedron given Surface-to-volume ratio (A/V)
side_a = (4*sqrt(11))/(surface to volume ratio*sqrt(2)) Go
Area of triakis tetrahedron given surface-volume-ratio
area = (3/5)*(sqrt(11/2))*(4/surface to volume ratio)^2 Go
Number Of Edges
no_of_edges = Number Of Faces +Number Of Vertices-2 Go
Value of E in Euler's formula
no_of_edges = Number of faces+Number Of Vertices-2 Go
Number Of Faces
no_of_faces = 2+Number Of Edges-Number Of Vertices Go
Midsphere radius of triakis tetrahedron given surface-volume-ratio
radius = sqrt(11)/surface to volume ratio Go
Insphere radius of triakis tetrahedron given surface-volume-ratio
radius = 3/surface to volume ratio 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 surface-to-volume ratio Formula

surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*((((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)))^2)
SA = (n/2)*(cot(pi/n)+sqrt(3))*((((12*(sin(pi/n))^2)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^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 surface-to-volume ratio?

Surface area of Antiprism given surface-to-volume ratio calculator uses surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*((((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)))^2) to calculate the Surface Area, The Surface area of Antiprism given surface-to-volume ratio 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 surface-to-volume ratio using this online calculator? To use this online calculator for Surface area of Antiprism given surface-to-volume ratio, enter Number Of Vertices (n) and surface to volume ratio (r) and hit the calculate button. Here is how the Surface area of Antiprism given surface-to-volume ratio calculation can be explained with given input values -> NaN = (1/2)*(cot(pi/1)+sqrt(3))*((((12*(sin(pi/1))^2)*(1/2)*(cot(pi/1)+sqrt(3)))/((1*sqrt(4*(cos(pi/(2*1))^2)-1)*(sin((3*pi)/(2*1)))*0.5)))^2).

### FAQ

What is Surface area of Antiprism given surface-to-volume ratio?
The Surface area of Antiprism given surface-to-volume ratio 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)*(n/2)*(cot(pi/n)+sqrt(3)))/((n*sqrt(4*(cos(pi/(2*n))^2)-1)*(sin((3*pi)/(2*n)))*r)))^2) or surface_area = (Number Of Vertices/2)*(cot(pi/Number Of Vertices)+sqrt(3))*((((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)))^2). Number Of Vertices is the number of vertices in the given two dimensional figure and surface to volume ratio is fraction of surface to volume.
How to calculate Surface area of Antiprism given surface-to-volume ratio?
The Surface area of Antiprism given surface-to-volume ratio 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)*(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)))^2). To calculate Surface area of Antiprism given surface-to-volume ratio, you need Number Of Vertices (n) and surface to volume ratio (r). With our tool, you need to enter the respective value for Number Of Vertices and 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 Surface Area?
In this formula, Surface Area uses Number Of Vertices and surface to volume ratio. 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)