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Long edge of pentagonal trapezohedron given surface-to-volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
side_b = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))
b = ((sqrt(5)+1)/2)*(((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
b = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r)) --> ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5))
Evaluating ... ...
b = 14.1068460550194
STEP 3: Convert Result to Output's Unit
14.1068460550194 Meter --> No Conversion Required
FINAL ANSWER
14.1068460550194 Meter <-- Side B
(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

side b of a triangle
side_b = sqrt(Side A^2+Side C^2-2*Side A*Side C*cos(Angle B)) Go
Second side of kite given both diagonals
side_b = sqrt(((Diagonal/2)^2)+(symmetry Diagonal-Distance from center to a point)^2) Go
Side of a parallelogram when diagonal and the other side is given
side_b = sqrt(2*(Diagonal 1)^2+2*(Diagonal 2)^2-4*(Side A)^2)/2 Go
Side b of parallelogram when diagonal and sides are given
side_b = sqrt((Diagonal 1^2+Diagonal 2^2-2*Side A^2)/2) Go
Leg b of right triangle given radius & other leg of circumscribed circle of a right triangle
side_b = sqrt(((4)*(Radius)^2)-(Side A)^2) Go
side b of rectangle given radius of the circumscribed circle of a rectangle
side_b = sqrt(((4)*(Radius)^2)-(Side A)^2) Go
Side of parallelogram BC from height measured at right angle form other side
side_b = Height of column1/sin(Angle B) Go
Side of parallelogram BC from height measured at right angle form that side
side_b = Height/sin(Angle A) Go
Side of the parallelogram when the height and sine of an angle are given
side_b = Height/sin(Theta) Go
Second side of kite given perimeter and other side
side_b = (Perimeter/2)-Side A Go
Side of the parallelogram when the area and height of the parallelogram are given
side_b = Area/Height Go

Long edge of pentagonal trapezohedron given surface-to-volume ratio Formula

side_b = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))
b = ((sqrt(5)+1)/2)*(((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 Long edge of pentagonal trapezohedron given surface-to-volume ratio?

Long edge of pentagonal trapezohedron given surface-to-volume ratio calculator uses side_b = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio)) to calculate the Side B, The Long edge of pentagonal trapezohedron given surface-to-volume ratio formula is defined as a straight line joining two adjacent vertices of pentagonal trapezohedron. Where, a =trapezohedron pentagonal edge. Side B and is denoted by b symbol.

How to calculate Long edge of pentagonal trapezohedron given surface-to-volume ratio using this online calculator? To use this online calculator for Long edge of pentagonal trapezohedron given surface-to-volume ratio, enter surface to volume ratio (r) and hit the calculate button. Here is how the Long edge of pentagonal trapezohedron given surface-to-volume ratio calculation can be explained with given input values -> 14.10685 = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5)).

FAQ

What is Long edge of pentagonal trapezohedron given surface-to-volume ratio?
The Long edge of pentagonal trapezohedron given surface-to-volume ratio formula is defined as a straight line joining two adjacent vertices of pentagonal trapezohedron. Where, a =trapezohedron pentagonal edge and is represented as b = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r)) or side_b = ((sqrt(5)+1)/2)*(((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 Long edge of pentagonal trapezohedron given surface-to-volume ratio?
The Long edge of pentagonal trapezohedron given surface-to-volume ratio formula is defined as a straight line joining two adjacent vertices of pentagonal trapezohedron. Where, a =trapezohedron pentagonal edge is calculated using side_b = ((sqrt(5)+1)/2)*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio)). To calculate Long edge 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 Side B?
In this formula, Side B uses surface to volume ratio. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • side_b = sqrt(Side A^2+Side C^2-2*Side A*Side C*cos(Angle B))
  • side_b = sqrt(2*(Diagonal 1)^2+2*(Diagonal 2)^2-4*(Side A)^2)/2
  • side_b = Height/sin(Theta)
  • side_b = Area/Height
  • side_b = Height/sin(Angle A)
  • side_b = Height of column1/sin(Angle B)
  • side_b = sqrt((Diagonal 1^2+Diagonal 2^2-2*Side A^2)/2)
  • side_b = sqrt(((4)*(Radius)^2)-(Side A)^2)
  • side_b = sqrt(((4)*(Radius)^2)-(Side A)^2)
  • side_b = sqrt(((Diagonal/2)^2)+(symmetry Diagonal-Distance from center to a point)^2)
  • side_b = (Perimeter/2)-Side A
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