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Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*Height))
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*h))
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 = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*h)) --> ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*12))
Evaluating ... ...
r = 0.129623211575948
STEP 3: Convert Result to Output's Unit
0.129623211575948 Hundred --> No Conversion Required
0.129623211575948 Hundred <-- surface to volume ratio
(Calculation completed in 00.016 seconds)

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

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Lateral Surface Area of a Cone
Total Surface Area of a Cylinder
Lateral Surface Area of a Cylinder
Volume of a Circular Cone
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
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-volume-ratio of triakis tetrahedron given Midsphere radius
Surface-to-volume ratio of Rhombic Dodecahedron given Insphere radius
surface-volume-ratio of triakis tetrahedron given Insphere radius

Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) Formula

surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*Height))
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*h))

What is Great Dodecahedron?

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter–Dynkin diagram of. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp)?

Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) calculator uses surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*Height)) to calculate the surface to volume ratio, The Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) formula is defined as what part of total volume of Great Dodecahedron is its total surface area. surface to volume ratio and is denoted by r symbol.

How to calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) using this online calculator? To use this online calculator for Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp), enter Height (h) and hit the calculate button. Here is how the Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) calculation can be explained with given input values -> 0.129623 = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*12)).

FAQ

What is Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) formula is defined as what part of total volume of Great Dodecahedron is its total surface area and is represented as r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*h)) or surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*Height)). Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp) formula is defined as what part of total volume of Great Dodecahedron is its total surface area is calculated using surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(3)*(3-sqrt(5)))/(6*Height)). To calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Pyramid height (hp), 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)))