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Volume of pentagonal trapezohedron given surface-to-volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^3)
V = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^3)
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
surface to volume ratio - surface to volume ratio is fraction of surface to volume. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
surface to volume ratio: 0.5 Hundred --> 0.5 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^3) --> (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5))^3)
Evaluating ... ...
V = 1445.84219438084
STEP 3: Convert Result to Output's Unit
1445.84219438084 Cubic Meter --> No Conversion Required
FINAL ANSWER
1445.84219438084 Cubic Meter <-- Volume
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

volume of Rhombic Dodecahedron given Surface-to-volume ratio
volume = (16/9)*sqrt(3)*((9*sqrt(2))/(2*sqrt(3)*surface to volume ratio))^3 Go
Volume of triakis tetrahedron given surface-volume-ratio
volume = (3/20)*sqrt(2)*((4*sqrt(11))/(surface to volume ratio*sqrt(2)))^3 Go
side given Surface-to-volume ratio (A/V) of Rhombic Triacontahedron
side = (3*sqrt(5))/(surface to volume ratio*(sqrt(5+(2*sqrt(5))))) Go
height of triakis tetrahedron given surface-volime-ratio
height = (3/5)*(sqrt(6))*(4/surface to volume ratio)*(sqrt(11/2)) Go
edge length of Rhombic Dodecahedron given Surface-to-volume ratio
side_a = (9*sqrt(2))/(2*sqrt(3)*surface to volume ratio) Go
edge length of tetrahedron(a) of triakis tetrahedron given Surface-to-volume ratio (A/V)
side_a = (4*sqrt(11))/(surface to volume ratio*sqrt(2)) Go
Area of triakis tetrahedron given surface-volume-ratio
area = (3/5)*(sqrt(11/2))*(4/surface to volume ratio)^2 Go
Area of Rhombic Dodecahedron given Surface-to-volume ratio
area = (108*sqrt(2))/((surface to volume ratio)^2) Go
Midsphere radius of Rhombic Dodecahedron given Surface-to-volume ratio
radius = (6/sqrt(3))*(1/surface to volume ratio) Go
Midsphere radius of triakis tetrahedron given surface-volume-ratio
radius = sqrt(11)/surface to volume ratio Go
Insphere radius of triakis tetrahedron given surface-volume-ratio
radius = 3/surface to volume ratio 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 pentagonal trapezohedron given surface-to-volume ratio Formula

volume = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^3)
V = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^3)

What is a trapezohedron?

The n-gonal trapezohedron, antidipyramid, antibipyramid, or deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of the n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (also called deltoids). The n-gon part of the name does not refer to faces here but to two arrangements of vertices around an axis of symmetry. The dual n-gonal antiprism has two actual n-gon faces. An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.

How to Calculate Volume of pentagonal trapezohedron given surface-to-volume ratio?

Volume of pentagonal trapezohedron given surface-to-volume ratio calculator uses volume = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^3) to calculate the Volume, The Volume of pentagonal trapezohedron given surface-to-volume ratio formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of pentagonal trapezohedron. Volume and is denoted by V symbol.

How to calculate Volume of pentagonal trapezohedron given surface-to-volume ratio using this online calculator? To use this online calculator for Volume of pentagonal trapezohedron given surface-to-volume ratio, enter surface to volume ratio (r) and hit the calculate button. Here is how the Volume of pentagonal trapezohedron given surface-to-volume ratio calculation can be explained with given input values -> 1445.842 = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5))^3).

FAQ

What is Volume of pentagonal trapezohedron given surface-to-volume ratio?
The Volume of pentagonal trapezohedron given surface-to-volume ratio formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of pentagonal trapezohedron and is represented as V = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^3) or volume = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^3). surface to volume ratio is fraction of surface to volume.
How to calculate Volume of pentagonal trapezohedron given surface-to-volume ratio?
The Volume of pentagonal trapezohedron given surface-to-volume ratio formula is defined as the quantity of three-dimensional space enclosed by a closed surface where a = edge length of pentagonal trapezohedron is calculated using volume = (5/12)*(3+sqrt(5))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^3). To calculate Volume of pentagonal trapezohedron given surface-to-volume ratio, you need surface to volume ratio (r). With our tool, you need to enter the respective value for surface to volume ratio 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 surface to volume ratio. 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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