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## Surface-to-volume ratio of Antiprism given height Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = ((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)))*(Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))))
r = ((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)))*(h/(sqrt(1-((sec(pi/(2*n)))^2)/4)))))
This formula uses 2 Constants, 5 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sin - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(Angle)
cot - Trigonometric cotangent function, cot(Angle)
sec - Trigonometric secant function, sec(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.
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
Height: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = ((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)))*(h/(sqrt(1-((sec(pi/(2*n)))^2)/4))))) --> ((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)))*(12/(sqrt(1-((sec(pi/(2*1)))^2)/4)))))
Evaluating ... ...
r = NaN
STEP 3: Convert Result to Output's Unit
NaN Hundred --> No Conversion Required
NaN Hundred <-- surface to volume ratio
(Calculation completed in 00.062 seconds)

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

Volume of a Conical Frustum
Total Surface Area of a Cone
Lateral Surface Area of a Cone
Total Surface Area of a Cylinder
Lateral Surface Area of a Cylinder
lateral_surface_area = 2*pi*Radius*Height Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Parallelogram when base and height are given
area = Base*Height Go

## < 11 Other formulas that calculate the same Output

surface-volume-ratio of triakis tetrahedron given area
surface_to_volume_ratio = 4*(sqrt(11/2))*(sqrt((3*sqrt(11))/(5*Area))) Go
Surface-to-volume ratio (A/V) given side of Rhombic Triacontahedron
surface_to_volume_ratio = (3*sqrt(5))/(Side*(sqrt(5+(2*sqrt(5))))) Go
surface-volume-ratio of triakis tetrahedron given volume
surface_to_volume_ratio = 4*(sqrt(11/2))*(((3*sqrt(2))/(20*Volume))^(1/3)) Go
surface-volume-ratio of triakis tetrahedron given height
surface_to_volume_ratio = 4*(sqrt(11/2))*((3*sqrt(6))/(5*Height)) Go
Surface-to-volume ratio of Rhombic Dodecahedron given edge length
surface_to_volume_ratio = (9*sqrt(2))/(2*sqrt(3)*Side A) Go
Surface-to-volume ratio (A/V) of triakis tetrahedron given edge length of tetrahedron(a)
surface_to_volume_ratio = (4*sqrt(11))/(Side A*sqrt(2)) Go
surface-volume-ratio of triakis tetrahedron given Edge length of pyramid(b)
surface_to_volume_ratio = 4*(sqrt(11/2))*(3/(5*Side B)) Go
Surface-to-volume ratio of Rhombic Dodecahedron given Midsphere radius
surface_to_volume_ratio = (6/(sqrt(3)*Radius)) Go
surface-volume-ratio of triakis tetrahedron given Midsphere radius
surface_to_volume_ratio = sqrt(11)/Radius Go
Surface-to-volume ratio of Rhombic Dodecahedron given Insphere radius
surface_to_volume_ratio = (3/Radius) Go
surface-volume-ratio of triakis tetrahedron given Insphere radius
surface_to_volume_ratio = 3/Radius Go

### Surface-to-volume ratio of Antiprism given height Formula

surface_to_volume_ratio = ((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)))*(Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)))))
r = ((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)))*(h/(sqrt(1-((sec(pi/(2*n)))^2)/4)))))

## 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-to-volume ratio of Antiprism given height?

Surface-to-volume ratio of Antiprism given height calculator uses surface_to_volume_ratio = ((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)))*(Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4))))) to calculate the surface to volume ratio, The Surface-to-volume ratio of Antiprism given height formula is defined as the ratio of surface area to volume of Antiprism, where a = Antiprism edge. surface to volume ratio and is denoted by r symbol.

How to calculate Surface-to-volume ratio of Antiprism given height using this online calculator? To use this online calculator for Surface-to-volume ratio of Antiprism given height, enter Number Of Vertices (n) and Height (h) and hit the calculate button. Here is how the Surface-to-volume ratio of Antiprism given height calculation can be explained with given input values -> NaN = ((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)))*(12/(sqrt(1-((sec(pi/(2*1)))^2)/4))))).

### FAQ

What is Surface-to-volume ratio of Antiprism given height?
The Surface-to-volume ratio of Antiprism given height formula is defined as the ratio of surface area to volume of Antiprism, where a = Antiprism edge and is represented as r = ((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)))*(h/(sqrt(1-((sec(pi/(2*n)))^2)/4))))) or surface_to_volume_ratio = ((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)))*(Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4))))). Number Of Vertices is the number of vertices in the given two dimensional figure and Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Surface-to-volume ratio of Antiprism given height?
The Surface-to-volume ratio of Antiprism given height formula is defined as the ratio of surface area to volume of Antiprism, where a = Antiprism edge is calculated using surface_to_volume_ratio = ((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)))*(Height/(sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4))))). To calculate Surface-to-volume ratio of Antiprism given height, you need Number Of Vertices (n) and Height (h). With our tool, you need to enter the respective value for Number Of Vertices and Height 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 to volume ratio?
In this formula, surface to volume ratio uses Number Of Vertices and Height. We can use 11 other way(s) to calculate the same, which is/are as follows -
• surface_to_volume_ratio = (3*sqrt(5))/(Side*(sqrt(5+(2*sqrt(5)))))
• surface_to_volume_ratio = (4*sqrt(11))/(Side A*sqrt(2))
• surface_to_volume_ratio = 4*(sqrt(11/2))*(3/(5*Side B))
• surface_to_volume_ratio = 4*(sqrt(11/2))*((3*sqrt(6))/(5*Height))
• surface_to_volume_ratio = 4*(sqrt(11/2))*(sqrt((3*sqrt(11))/(5*Area)))
• surface_to_volume_ratio = 3/Radius
• surface_to_volume_ratio = sqrt(11)/Radius
• surface_to_volume_ratio = 4*(sqrt(11/2))*(((3*sqrt(2))/(20*Volume))^(1/3))
• surface_to_volume_ratio = (9*sqrt(2))/(2*sqrt(3)*Side A)
• surface_to_volume_ratio = (3/Radius)
• surface_to_volume_ratio = (6/(sqrt(3)*Radius))
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