Volume of anticube given height Calculator

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3D Geometry	Anticube ↺

✖Height is the distance between the lowest and highest points of a person standing upright.ⓘ Height [h]

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✖Volume is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume of anticube given height [V]

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Mona Gladys

St Joseph's College (St Joseph's College), Bengaluru

Mona Gladys has created this Calculator and 1000+ more calculators!

Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Volume of anticube given height Solution

STEP 0: Pre-Calculation Summary

Formula Used

volume = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((Height/(sqrt(1-(1/(2+sqrt(2))))))^3)
V = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((h/(sqrt(1-(1/(2+sqrt(2))))))^3)
This formula uses 1 Functions, 1 Variables

Functions Used

sqrt - Squre root function, sqrt(Number)

Variables Used

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

Height: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((h/(sqrt(1-(1/(2+sqrt(2))))))^3) --> (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((12/(sqrt(1-(1/(2+sqrt(2))))))^3)

Evaluating ... ...

V = 2781.17402385381

STEP 3: Convert Result to Output's Unit

2781.17402385381 Cubic Meter --> No Conversion Required

FINAL ANSWER

2781.17402385381 Cubic Meter <-- Volume

(Calculation completed in 00.003 seconds)

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

Volume of a Conical Frustum

volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go

Total Surface Area of a Cone

total_surface_area = pi*Radius*(Radius+sqrt(Radius^2+Height^2)) Go

Lateral Surface Area of a Cone

lateral_surface_area = pi*Radius*sqrt(Radius^2+Height^2) Go

Total Surface Area of a Cylinder

total_surface_area = 2*pi*Radius*(Height+Radius) Go

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

Volume of a Conical Frustum

volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go

Volume of a Capsule

volume = pi*(Radius)^2*((4/3)*Radius+Side) Go

Volume of a Circular Cone

volume = (1/3)*pi*(Radius)^2*Height Go

Volume of a Circular Cylinder

volume = pi*(Radius)^2*Height Go

Volume of a Rectangular Prism

volume = Width*Height*Length Go

Volume of Regular Dodecahedron

volume = ((15+(7*sqrt(5)))*Side^3)/4 Go

Volume of Regular Icosahedron

volume = (5*(3+sqrt(5))*Side^3)/12 Go

Volume of a Hemisphere

volume = (2/3)*pi*(Radius)^3 Go

Volume of a Sphere

volume = (4/3)*pi*(Radius)^3 Go

Volume of a Pyramid

volume = (1/3)*Side^2*Height Go

Volume of a Cube

volume = Side^3 Go

Volume of anticube given height Formula

volume = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((Height/(sqrt(1-(1/(2+sqrt(2))))))^3)
V = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((h/(sqrt(1-(1/(2+sqrt(2))))))^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 Volume of anticube given height?

Volume of anticube given height calculator uses volume = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((Height/(sqrt(1-(1/(2+sqrt(2))))))^3) to calculate the Volume, The Volume of anticube given height formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of anticube. Volume and is denoted by V symbol.

How to calculate Volume of anticube given height using this online calculator? To use this online calculator for Volume of anticube given height, enter Height (h) and hit the calculate button. Here is how the Volume of anticube given height calculation can be explained with given input values -> 2781.174 = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((12/(sqrt(1-(1/(2+sqrt(2))))))^3).

FAQ

What is Volume of anticube given height?

The Volume of anticube given height formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of anticube and is represented as V = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((h/(sqrt(1-(1/(2+sqrt(2))))))^3) or volume = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((Height/(sqrt(1-(1/(2+sqrt(2))))))^3). Height is the distance between the lowest and highest points of a person standing upright.

How to calculate Volume of anticube given height?

The Volume of anticube given height formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of anticube is calculated using volume = (1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*((Height/(sqrt(1-(1/(2+sqrt(2))))))^3). To calculate Volume of anticube given height, you need Height (h). With our tool, you need to enter the respective value for 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 Volume?

In this formula, Volume uses Height. We can use 11 other way(s) to calculate the same, which is/are as follows -

volume = pi*(Radius)^2*((4/3)*Radius+Side)
volume = (1/3)*pi*(Radius)^2*Height
volume = pi*(Radius)^2*Height
volume = Side^3
volume = (2/3)*pi*(Radius)^3
volume = (4/3)*pi*(Radius)^3
volume = (1/3)*Side^2*Height
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2))
volume = Width*Height*Length
volume = ((15+(7*sqrt(5)))*Side^3)/4
volume = (5*(3+sqrt(5))*Side^3)/12

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