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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)

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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