Surface to Volume Ratio of Antiprism given Height Calculator

✖Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.ⓘ Number of Vertices of Antiprism [N_Vertices]			+10% -10%
✖Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.ⓘ Height of Antiprism [h]			+10% -10%

✖Surface to Volume Ratio of Antiprism is the fraction of the surface area to volume of Antiprism.ⓘ Surface to Volume Ratio of Antiprism given Height [R_A/V]

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Surface to Volume Ratio of Antiprism given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))
R_A/V = (6*(sin(pi/N_Vertices))^2*(cot(pi/N_Vertices)+sqrt(3)))/(sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)))
This formula uses 1 Constants, 5 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Surface to Volume Ratio of Antiprism - (Measured in 1 per Meter) - Surface to Volume Ratio of Antiprism is the fraction of the surface area to volume of Antiprism.
Number of Vertices of Antiprism - Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.
Height of Antiprism - (Measured in Meter) - Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

STEP 1: Convert Input(s) to Base Unit

Number of Vertices of Antiprism: 5 --> No Conversion Required
Height of Antiprism: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (6*(sin(pi/N_Vertices))^2*(cot(pi/N_Vertices)+sqrt(3)))/(sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4))) --> (6*(sin(pi/5))^2*(cot(pi/5)+sqrt(3)))/(sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*8/(sqrt(1-((sec(pi/(2*5)))^2)/4)))

Evaluating ... ...

R_A/V = 0.523414971827094

STEP 3: Convert Result to Output's Unit

0.523414971827094 1 per Meter --> No Conversion Required

FINAL ANSWER

0.523414971827094 ≈ 0.523415 1 per Meter <-- Surface to Volume Ratio of Antiprism

(Calculation completed in 00.004 seconds)

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< Surface to Volume Ratio of Antiprism Calculators

Surface to Volume Ratio of Antiprism given Volume

LaTeX Go Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3))

Surface to Volume Ratio of Antiprism given Total Surface Area

LaTeX Go Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))

Surface to Volume Ratio of Antiprism given Height

LaTeX Go Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))

Surface to Volume Ratio of Antiprism

Surface to Volume Ratio of Antiprism given Height Formula

LaTeX Go

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 of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))) to calculate the Surface to Volume Ratio of Antiprism, The Surface to Volume Ratio of Antiprism given Height formula is defined as the fraction of the surface area to the volume of Antiprism, calculated using the height of Antiprism. Surface to Volume Ratio of Antiprism is denoted by R_A/V 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 of Antiprism (N_Vertices) & Height of Antiprism (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 -> 0.523415 = (6*(sin(pi/5))^2*(cot(pi/5)+sqrt(3)))/(sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*8/(sqrt(1-((sec(pi/(2*5)))^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 fraction of the surface area to the volume of Antiprism, calculated using the height of Antiprism and is represented as R_A/V = (6*(sin(pi/N_Vertices))^2*(cot(pi/N_Vertices)+sqrt(3)))/(sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4))) or Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))). Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism & Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

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 fraction of the surface area to the volume of Antiprism, calculated using the height of Antiprism is calculated using Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4))). To calculate Surface to Volume Ratio of Antiprism given Height, you need Number of Vertices of Antiprism (N_Vertices) & Height of Antiprism (h). With our tool, you need to enter the respective value for Number of Vertices of Antiprism & Height of Antiprism 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 of Antiprism?

In this formula, Surface to Volume Ratio of Antiprism uses Number of Vertices of Antiprism & Height of Antiprism. We can use 3 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Edge Length of Antiprism)
Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))
Surface to Volume Ratio of Antiprism = (6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3))

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