Height of Anticube given Total Surface Area Calculator

✖Total Surface Area of Anticube is defined as the measure of the total amount of 2d space occupied by all the faces of the Anticube.ⓘ Total Surface Area of Anticube [TSA]

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✖Height of Anticube is defined as the measure of the vertical distance between the top and bottom square-shaped faces.ⓘ Height of Anticube given Total Surface Area [h]

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Formula

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Height of Anticube given Total Surface Area

Formula

`"h" = sqrt(1-1/(2+sqrt(2)))*sqrt("TSA"/(2*(1+sqrt(3))))`

Example

`"8.398106m"=sqrt(1-1/(2+sqrt(2)))*sqrt("545m²"/(2*(1+sqrt(3))))`

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Height of Anticube given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Anticube = sqrt(1-1/(2+sqrt(2)))*sqrt(Total Surface Area of Anticube/(2*(1+sqrt(3))))
h = sqrt(1-1/(2+sqrt(2)))*sqrt(TSA/(2*(1+sqrt(3))))
This formula uses 1 Functions, 2 Variables

Functions Used

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

Height of Anticube - (Measured in Meter) - Height of Anticube is defined as the measure of the vertical distance between the top and bottom square-shaped faces.
Total Surface Area of Anticube - (Measured in Square Meter) - Total Surface Area of Anticube is defined as the measure of the total amount of 2d space occupied by all the faces of the Anticube.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Anticube: 545 Square Meter --> 545 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(1-1/(2+sqrt(2)))*sqrt(TSA/(2*(1+sqrt(3)))) --> sqrt(1-1/(2+sqrt(2)))*sqrt(545/(2*(1+sqrt(3))))

Evaluating ... ...

h = 8.39810632169163

STEP 3: Convert Result to Output's Unit

8.39810632169163 Meter --> No Conversion Required

FINAL ANSWER

8.39810632169163 ≈ 8.398106 Meter <-- Height of Anticube

(Calculation completed in 00.004 seconds)

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< 4 Height of Anticube Calculators

Height of Anticube given Surface to Volume Ratio

Go Height of Anticube = sqrt(1-1/(2+sqrt(2)))*(2*(1+sqrt(3)))/(1/3*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Surface to Volume Ratio of Anticube)

Height of Anticube given Volume

Go Height of Anticube = sqrt(1-1/(2+sqrt(2)))*((3*Volume of Anticube)/(sqrt(1+sqrt(2))*sqrt(2+sqrt(2))))^(1/3)

Height of Anticube given Total Surface Area

Go Height of Anticube = sqrt(1-1/(2+sqrt(2)))*sqrt(Total Surface Area of Anticube/(2*(1+sqrt(3))))

Height of Anticube

Go Height of Anticube = sqrt(1-1/(2+sqrt(2)))*Edge Length of Anticube

Height of Anticube given Total Surface Area Formula

Height of Anticube = sqrt(1-1/(2+sqrt(2)))*sqrt(Total Surface Area of Anticube/(2*(1+sqrt(3))))
h = sqrt(1-1/(2+sqrt(2)))*sqrt(TSA/(2*(1+sqrt(3))))

What is an Anticube?

In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It is also known as an anticube. If all its faces are regular, it is a semiregular polyhedron. When eight points are distributed on the surface of a sphere with the aim of maximising the distance between them in some sense, then the resulting shape corresponds to a square anti-prism rather than a cube. Different examples include maximising the distance to the nearest point, or using electrons to maximise the sum of all reciprocals of squares of distances.

How to Calculate Height of Anticube given Total Surface Area?

Height of Anticube given Total Surface Area calculator uses Height of Anticube = sqrt(1-1/(2+sqrt(2)))*sqrt(Total Surface Area of Anticube/(2*(1+sqrt(3)))) to calculate the Height of Anticube, The Height of Anticube given Total Surface Area formula is defined as the measure of vertical distance from one top to bottom face of the Anticube, calculated using total surface area. Height of Anticube is denoted by h symbol.

How to calculate Height of Anticube given Total Surface Area using this online calculator? To use this online calculator for Height of Anticube given Total Surface Area, enter Total Surface Area of Anticube (TSA) and hit the calculate button. Here is how the Height of Anticube given Total Surface Area calculation can be explained with given input values -> 8.398106 = sqrt(1-1/(2+sqrt(2)))*sqrt(545/(2*(1+sqrt(3)))).

FAQ

What is Height of Anticube given Total Surface Area?

The Height of Anticube given Total Surface Area formula is defined as the measure of vertical distance from one top to bottom face of the Anticube, calculated using total surface area and is represented as h = sqrt(1-1/(2+sqrt(2)))*sqrt(TSA/(2*(1+sqrt(3)))) or Height of Anticube = sqrt(1-1/(2+sqrt(2)))*sqrt(Total Surface Area of Anticube/(2*(1+sqrt(3)))). Total Surface Area of Anticube is defined as the measure of the total amount of 2d space occupied by all the faces of the Anticube.

How to calculate Height of Anticube given Total Surface Area?

The Height of Anticube given Total Surface Area formula is defined as the measure of vertical distance from one top to bottom face of the Anticube, calculated using total surface area is calculated using Height of Anticube = sqrt(1-1/(2+sqrt(2)))*sqrt(Total Surface Area of Anticube/(2*(1+sqrt(3)))). To calculate Height of Anticube given Total Surface Area, you need Total Surface Area of Anticube (TSA). With our tool, you need to enter the respective value for Total Surface Area of Anticube 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 Height of Anticube?

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

Height of Anticube = sqrt(1-1/(2+sqrt(2)))*Edge Length of Anticube
Height of Anticube = sqrt(1-1/(2+sqrt(2)))*((3*Volume of Anticube)/(sqrt(1+sqrt(2))*sqrt(2+sqrt(2))))^(1/3)
Height of Anticube = sqrt(1-1/(2+sqrt(2)))*(2*(1+sqrt(3)))/(1/3*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Surface to Volume Ratio of Anticube)

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