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Total Surface Area of Antiprism given Volume Formula

GoTotal Surface Area of Antiprism Formula

GoTotal Surface Area of Antiprism given Height Formula

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The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism. Check FAQs

TSA = \frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot V}{N Vertices \cdot \sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1}})}^{\frac{2}{3}}

TSA - Total Surface Area of Antiprism?N_Vertices - Number of Vertices of Antiprism?V - Volume of Antiprism?π - Archimedes' constant?

Total Surface Area of Antiprism given Volume Example

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Here is how the Total Surface Area of Antiprism given Volume equation looks like with Values.

Here is how the Total Surface Area of Antiprism given Volume equation looks like with Units.

Here is how the Total Surface Area of Antiprism given Volume equation looks like.

777.5382 = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{2}{3}}

777.5382m² = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580m³}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{2}{3}}

777.5382 = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{2}{3}}

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Total Surface Area of Antiprism given Volume Solution

Follow our step by step solution on how to calculate Total Surface Area of Antiprism given Volume?

FIRST Step Consider the formula

TSA = \frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot V}{N Vertices \cdot \sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1}})}^{\frac{2}{3}}

Next Step Substitute values of Variables

∴

TSA = \frac{5}{2} \cdot (\cot (\frac{π}{5}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{π}{5}))}^{2} \cdot 1580m³}{5 \cdot \sin (\frac{3 \cdot π}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot 5})}^{2}) - 1}})}^{\frac{2}{3}}

Next Step Substitute values of Constants

∴

TSA = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580m³}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{2}{3}}

Next Step Prepare to Evaluate

∴

TSA = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{12 \cdot {(\sin (\frac{3.1416}{5}))}^{2} \cdot 1580}{5 \cdot \sin (\frac{3 \cdot 3.1416}{2 \cdot 5}) \cdot \sqrt{4 \cdot ({\cos (\frac{3.1416}{2 \cdot 5})}^{2}) - 1}})}^{\frac{2}{3}}

Next Step Evaluate

∴

TSA = 777.538241181199m²

LAST Step Rounding Answer

∴

TSA = 777.5382m²

Total Surface Area of Antiprism given Volume Formula Elements

Variables

Constants

Functions

Total Surface Area of 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.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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.

Symbol: N_Vertices

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Vertices of Antiprism

Volume of Antiprism

Volume of Antiprism is defined as the quantity of three-dimensional space enclosed by a closed surface of Antiprism.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Antiprism

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Antiprism

Go Total Surface Area of Antiprism

TSA = \frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3}) \cdot {l e}^{2}

Go Total Surface Area of Antiprism given Height

TSA = \frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3}) \cdot {(\frac{h}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}}})}^{2}

Go Total Surface Area of Antiprism given Surface to Volume Ratio

TSA = \frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3}) \cdot {(\frac{6 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}{\sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1} \cdot R A/V})}^{2}

How to Evaluate Total Surface Area of Antiprism given Volume?

Total Surface Area of Antiprism given Volume evaluator uses Total Surface Area of Antiprism = Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(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)))^(2/3) to evaluate the Total Surface Area of Antiprism, The Total Surface Area of Antiprism given Volume formula is defined as the measure of the total 2d space occupied by all the faces of the Antiprism, calculated using the volume of Antiprism. Total Surface Area of Antiprism is denoted by TSA symbol.

How to evaluate Total Surface Area of Antiprism given Volume using this online evaluator? To use this online evaluator for Total Surface Area of Antiprism given Volume, enter Number of Vertices of Antiprism (N_Vertices) & Volume of Antiprism (V) and hit the calculate button.

FAQs on Total Surface Area of Antiprism given Volume

What is the formula to find Total Surface Area of Antiprism given Volume?

The formula of Total Surface Area of Antiprism given Volume is expressed as Total Surface Area of Antiprism = Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(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)))^(2/3). Here is an example- 777.5382 = 5/2*(cot(pi/5)+sqrt(3))*((12*(sin(pi/5))^2*1580)/(5*sin((3*pi)/(2*5))*sqrt(4*(cos(pi/(2*5))^2)-1)))^(2/3).

How to calculate Total Surface Area of Antiprism given Volume?

With Number of Vertices of Antiprism (N_Vertices) & Volume of Antiprism (V) we can find Total Surface Area of Antiprism given Volume using the formula - Total Surface Area of Antiprism = Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(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)))^(2/3). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos), Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Antiprism?

Here are the different ways to Calculate Total Surface Area of Antiprism-

Total Surface Area of Antiprism=Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))*Edge Length of Antiprism^2
Total Surface Area of Antiprism=Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))*(Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)))^2
Total Surface Area of Antiprism=Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))*((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))^2

Can the Total Surface Area of Antiprism given Volume be negative?

No, the Total Surface Area of Antiprism given Volume, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Antiprism given Volume?

Total Surface Area of Antiprism given Volume is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Antiprism given Volume can be measured.

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Total Surface Area of Antiprism given Volume Formula

​GoTotal Surface Area of Antiprism Formula

​GoTotal Surface Area of Antiprism given Height Formula

Total Surface Area of Antiprism given Volume Example

Total Surface Area of Antiprism given Volume Solution

Total Surface Area of Antiprism given Volume Formula Elements

Other Formulas to find Total Surface Area of Antiprism

How to Evaluate Total Surface Area of Antiprism given Volume?

FAQs on Total Surface Area of Antiprism given Volume

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GoTotal Surface Area of Antiprism Formula

GoTotal Surface Area of Antiprism given Height Formula