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

STEP 0: Pre-Calculation Summary
Formula Used
height = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))
h = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))
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
h = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r)) --> (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5))
Evaluating ... ...
h = 26.8328157299975
STEP 3: Convert Result to Output's Unit
26.8328157299975 Meter --> No Conversion Required
FINAL ANSWER
26.8328157299975 Meter <-- Height
(Calculation completed in 00.000 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

Height of a triangular prism when lateral surface area is given
height = Lateral Surface Area/(Side A+Side B+Side C) Go
Height of an isosceles trapezoid
height = sqrt(Side C^2-0.25*(Side A-Side B)^2) Go
Altitude of an isosceles triangle
height = sqrt((Side A)^2+((Side B)^2/4)) Go
Height of a triangular prism when base and volume are given
height = (2*Volume)/(Base*Length) Go
Height of a trapezoid when area and sum of parallel sides are given
height = (2*Area)/Sum of parallel sides of a trapezoid Go
Altitude of the largest right pyramid with a square base that can be inscribed in a sphere of radius a
height = 4*Radius of Sphere/3 Go
Height of Cone inscribed in a sphere for maximum volume of cone in terms of radius of sphere
height = 4*Radius of Sphere/3 Go
Height of Cone circumscribing a sphere such that volume of cone is minimum
height = 4*Radius of Sphere Go
Height of parabolic section that can be cut from a cone for maximum area of parabolic section
height = 0.75*Slant Height Go
Height of a circular cylinder of maximum convex surface area in a given circular cone
height = Height of Cone/2 Go
Height of Largest right circular cylinder that can be inscribed within a cone
height = Height of Cone/3 Go

Height of pentagonal trapezohedron given surface-to-volume ratio Formula

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

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 Height of pentagonal trapezohedron given surface-to-volume ratio?

Height of pentagonal trapezohedron given surface-to-volume ratio calculator uses height = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio)) to calculate the Height, The Height of pentagonal trapezohedron given surface-to-volume ratio formula is defined as the measure of vertical distance from one top to bottom face of pentagonal trapezohedron, where h = height of pentagonal trapezohedron. Height and is denoted by h symbol.

How to calculate Height of pentagonal trapezohedron given surface-to-volume ratio using this online calculator? To use this online calculator for Height of pentagonal trapezohedron given surface-to-volume ratio, enter surface to volume ratio (r) and hit the calculate button. Here is how the Height of pentagonal trapezohedron given surface-to-volume ratio calculation can be explained with given input values -> 26.83282 = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5)).

FAQ

What is Height of pentagonal trapezohedron given surface-to-volume ratio?
The Height of pentagonal trapezohedron given surface-to-volume ratio formula is defined as the measure of vertical distance from one top to bottom face of pentagonal trapezohedron, where h = height of pentagonal trapezohedron and is represented as h = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r)) or height = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio)). surface to volume ratio is fraction of surface to volume.
How to calculate Height of pentagonal trapezohedron given surface-to-volume ratio?
The Height of pentagonal trapezohedron given surface-to-volume ratio formula is defined as the measure of vertical distance from one top to bottom face of pentagonal trapezohedron, where h = height of pentagonal trapezohedron is calculated using height = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio)). To calculate Height 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 Height?
In this formula, Height uses surface to volume ratio. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • height = 4*Radius of Sphere/3
  • height = 4*Radius of Sphere
  • height = Height of Cone/3
  • height = 4*Radius of Sphere/3
  • height = Height of Cone/2
  • height = 0.75*Slant Height
  • height = sqrt(Side C^2-0.25*(Side A-Side B)^2)
  • height = (2*Area)/Sum of parallel sides of a trapezoid
  • height = sqrt((Side A)^2+((Side B)^2/4))
  • height = (2*Volume)/(Base*Length)
  • height = Lateral Surface Area/(Side A+Side B+Side C)
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