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Surface-to-volume ratio of anticube given height Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Height/(sqrt(1-(1/(2+sqrt(2))))))
r = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*h/(sqrt(1-(1/(2+sqrt(2))))))
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
r = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*h/(sqrt(1-(1/(2+sqrt(2)))))) --> (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*12/(sqrt(1-(1/(2+sqrt(2))))))
Evaluating ... ...
r = 0.40009957749537
STEP 3: Convert Result to Output's Unit
0.40009957749537 Hundred --> No Conversion Required
FINAL ANSWER
0.40009957749537 Hundred <-- surface to volume ratio
(Calculation completed in 00.016 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

surface-volume-ratio of triakis tetrahedron given area
surface_to_volume_ratio = 4*(sqrt(11/2))*(sqrt((3*sqrt(11))/(5*Area))) Go
Surface-to-volume ratio (A/V) given side of Rhombic Triacontahedron
surface_to_volume_ratio = (3*sqrt(5))/(Side*(sqrt(5+(2*sqrt(5))))) Go
surface-volume-ratio of triakis tetrahedron given volume
surface_to_volume_ratio = 4*(sqrt(11/2))*(((3*sqrt(2))/(20*Volume))^(1/3)) Go
surface-volume-ratio of triakis tetrahedron given height
surface_to_volume_ratio = 4*(sqrt(11/2))*((3*sqrt(6))/(5*Height)) Go
Surface-to-volume ratio of Rhombic Dodecahedron given edge length
surface_to_volume_ratio = (9*sqrt(2))/(2*sqrt(3)*Side A) Go
Surface-to-volume ratio (A/V) of triakis tetrahedron given edge length of tetrahedron(a)
surface_to_volume_ratio = (4*sqrt(11))/(Side A*sqrt(2)) Go
surface-volume-ratio of triakis tetrahedron given Edge length of pyramid(b)
surface_to_volume_ratio = 4*(sqrt(11/2))*(3/(5*Side B)) Go
Surface-to-volume ratio of Rhombic Dodecahedron given Midsphere radius
surface_to_volume_ratio = (6/(sqrt(3)*Radius)) Go
surface-volume-ratio of triakis tetrahedron given Midsphere radius
surface_to_volume_ratio = sqrt(11)/Radius Go
Surface-to-volume ratio of Rhombic Dodecahedron given Insphere radius
surface_to_volume_ratio = (3/Radius) Go
surface-volume-ratio of triakis tetrahedron given Insphere radius
surface_to_volume_ratio = 3/Radius Go

Surface-to-volume ratio of anticube given height Formula

surface_to_volume_ratio = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Height/(sqrt(1-(1/(2+sqrt(2))))))
r = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*h/(sqrt(1-(1/(2+sqrt(2))))))

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 Surface-to-volume ratio of anticube given height?

Surface-to-volume ratio of anticube given height calculator uses surface_to_volume_ratio = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Height/(sqrt(1-(1/(2+sqrt(2)))))) to calculate the surface to volume ratio, The Surface-to-volume ratio of anticube given height formula is defined as the ratio of surface area to volume of anticube, where a = anticube edge. surface to volume ratio and is denoted by r symbol.

How to calculate Surface-to-volume ratio of anticube given height using this online calculator? To use this online calculator for Surface-to-volume ratio of anticube given height, enter Height (h) and hit the calculate button. Here is how the Surface-to-volume ratio of anticube given height calculation can be explained with given input values -> 0.4001 = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*12/(sqrt(1-(1/(2+sqrt(2)))))).

FAQ

What is Surface-to-volume ratio of anticube given height?
The Surface-to-volume ratio of anticube given height formula is defined as the ratio of surface area to volume of anticube, where a = anticube edge and is represented as r = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*h/(sqrt(1-(1/(2+sqrt(2)))))) or surface_to_volume_ratio = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Height/(sqrt(1-(1/(2+sqrt(2)))))). Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Surface-to-volume ratio of anticube given height?
The Surface-to-volume ratio of anticube given height formula is defined as the ratio of surface area to volume of anticube, where a = anticube edge is calculated using surface_to_volume_ratio = (2*(1+sqrt(3)))/((1/3)*sqrt(1+sqrt(2))*sqrt(2+sqrt(2))*Height/(sqrt(1-(1/(2+sqrt(2)))))). To calculate Surface-to-volume ratio 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 surface to volume ratio?
In this formula, surface to volume ratio uses Height. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • surface_to_volume_ratio = (3*sqrt(5))/(Side*(sqrt(5+(2*sqrt(5)))))
  • surface_to_volume_ratio = (4*sqrt(11))/(Side A*sqrt(2))
  • surface_to_volume_ratio = 4*(sqrt(11/2))*(3/(5*Side B))
  • surface_to_volume_ratio = 4*(sqrt(11/2))*((3*sqrt(6))/(5*Height))
  • surface_to_volume_ratio = 4*(sqrt(11/2))*(sqrt((3*sqrt(11))/(5*Area)))
  • surface_to_volume_ratio = 3/Radius
  • surface_to_volume_ratio = sqrt(11)/Radius
  • surface_to_volume_ratio = 4*(sqrt(11/2))*(((3*sqrt(2))/(20*Volume))^(1/3))
  • surface_to_volume_ratio = (9*sqrt(2))/(2*sqrt(3)*Side A)
  • surface_to_volume_ratio = (3/Radius)
  • surface_to_volume_ratio = (6/(sqrt(3)*Radius))
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