Volume of Antiprism given Total Surface Area 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%
✖The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.ⓘ Total Surface Area of Antiprism [TSA]			+10% -10%

✖Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.ⓘ Volume of Antiprism given Total Surface Area [V]

⎘ Copy

👎

Formula

✖

Volume of Antiprism given Total Surface Area

Formula

`"V" = ("N"_{"Vertices"}*sin((3*pi)/(2*"N"_{"Vertices"}))*sqrt(4*(cos(pi/(2*"N"_{"Vertices"}))^2)-1)*(sqrt("TSA"/("N"_{"Vertices"}/2*(cot(pi/"N"_{"Vertices"})+sqrt(3)))))^3)/(12*(sin(pi/"N"_{"Vertices"}))^2)`

Example

`"1587.51m³"=("5"*sin((3*pi)/(2*"5"))*sqrt(4*(cos(pi/(2*"5"))^2)-1)*(sqrt("780m²"/("5"/2*(cot(pi/"5")+sqrt(3)))))^3)/(12*(sin(pi/"5"))^2)`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Volume of Antiprism given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)
V = (N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*(sqrt(TSA/(N_Vertices/2*(cot(pi/N_Vertices)+sqrt(3)))))^3)/(12*(sin(pi/N_Vertices))^2)
This formula uses 1 Constants, 4 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)
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

Volume of Antiprism - (Measured in Cubic Meter) - Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface 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.
Total Surface Area of Antiprism - (Measured in Square Meter) - The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.

STEP 1: Convert Input(s) to Base Unit

Number of Vertices of Antiprism: 5 --> No Conversion Required
Total Surface Area of Antiprism: 780 Square Meter --> 780 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*(sqrt(TSA/(N_Vertices/2*(cot(pi/N_Vertices)+sqrt(3)))))^3)/(12*(sin(pi/N_Vertices))^2) --> (5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*(sqrt(780/(5/2*(cot(pi/5)+sqrt(3)))))^3)/(12*(sin(pi/5))^2)

Evaluating ... ...

V = 1587.50957791706

STEP 3: Convert Result to Output's Unit

1587.50957791706 Cubic Meter --> No Conversion Required

FINAL ANSWER

1587.50957791706 ≈ 1587.51 Cubic Meter <-- Volume of Antiprism

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Antiprism » Volume of Antiprism » Volume of Antiprism given Total Surface Area

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< 4 Volume of Antiprism Calculators

Volume of Antiprism given Surface to Volume Ratio

Go 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)*((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)*Surface to Volume Ratio of Antiprism))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)

Volume of Antiprism given Total Surface Area

Go 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)

Volume of Antiprism given Height

Go 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)*(Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)

Volume of Antiprism

Go 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)*Edge Length of Antiprism^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)

Volume of Antiprism given Total 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 Total Surface Area?

Volume of Antiprism given Total Surface Area calculator uses 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2) to calculate the Volume of Antiprism, The Volume of Antiprism given Total Surface Area formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism, calculated using the total surface area of Antiprism. Volume of Antiprism is denoted by V symbol.

How to calculate Volume of Antiprism given Total Surface Area using this online calculator? To use this online calculator for Volume of Antiprism given Total Surface Area, enter Number of Vertices of Antiprism (N_Vertices) & Total Surface Area of Antiprism (TSA) and hit the calculate button. Here is how the Volume of Antiprism given Total Surface Area calculation can be explained with given input values -> 1587.51 = (5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)*(sqrt(780/(5/2*(cot(pi/5)+sqrt(3)))))^3)/(12*(sin(pi/5))^2).

FAQ

What is Volume of Antiprism given Total Surface Area?

The Volume of Antiprism given Total Surface Area formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism, calculated using the total surface area of Antiprism and is represented as V = (N_Vertices*sin((3*pi)/(2*N_Vertices))*sqrt(4*(cos(pi/(2*N_Vertices))^2)-1)*(sqrt(TSA/(N_Vertices/2*(cot(pi/N_Vertices)+sqrt(3)))))^3)/(12*(sin(pi/N_Vertices))^2) or 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2). Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism & The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.

How to calculate Volume of Antiprism given Total Surface Area?

The Volume of Antiprism given Total Surface Area formula is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism, calculated using the total surface area of Antiprism is calculated using 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)*(sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2). To calculate Volume of Antiprism given Total Surface Area, you need Number of Vertices of Antiprism (N_Vertices) & Total Surface Area of Antiprism (TSA). With our tool, you need to enter the respective value for Number of Vertices of Antiprism & Total Surface Area 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 Volume of Antiprism?

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

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)*Edge Length of Antiprism^3)/(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)*(Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))^3)/(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)*((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)*Surface to Volume Ratio of Antiprism))^3)/(12*(sin(pi/Number of Vertices of Antiprism))^2)

Home

FREE PDFs

🔍 Search