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Surface area of pentagonal trapezohedron given surface-to-volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_area = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^2)
SA = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^2)
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
SA = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^2) --> (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5))^2)
Evaluating ... ...
SA = 722.921097190418
STEP 3: Convert Result to Output's Unit
722.921097190418 Square Meter --> No Conversion Required
FINAL ANSWER
722.921097190418 Square Meter <-- Surface Area
(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

Surface Area of Cuboid
surface_area = 2*((Length*Height)+(Height*Breadth)+(Length*Breadth)) Go
Surface Area of a Rectangular Prism
surface_area = 2*(Length*Width+Length*Height+Width*Height) Go
Surface Area of triangular prism
surface_area = (Base*Height)+(2*Length*Side)+(Length*Base) Go
Surface Area of a Capsule
surface_area = 2*pi*Radius*(2*Radius+Side) Go
Surface Area of Prisms
surface_area = (2*Base Area)+(Height*Base Perimeter) Go
Surface Area of Dodecahedron
surface_area = 3*(sqrt(25+(10*sqrt(5))))*(Side^2) Go
Surface Area of Regular Octahedron
surface_area = 2*(sqrt(3))*(Side^2) Go
Surface Area of Icosahedron
surface_area = 5*(sqrt(3))*(Side^2) Go
Surface Area of Regular Tetrahedron
surface_area = (sqrt(3))*(Side^2) Go
Surface Area of a Sphere
surface_area = 4*pi*Radius^2 Go
Surface Area of a Cube
surface_area = 6*Side^2 Go

Surface area of pentagonal trapezohedron given surface-to-volume ratio Formula

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

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 Surface area of pentagonal trapezohedron given surface-to-volume ratio?

Surface area of pentagonal trapezohedron given surface-to-volume ratio calculator uses surface_area = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^2) to calculate the Surface Area, The Surface area of pentagonal trapezohedron given surface-to-volume ratio formula is defined as measure of the total area that the surface of the object occupies of a pentagonal trapezohedron, where a =pentagonal trapezohedron edge. Surface Area and is denoted by SA symbol.

How to calculate Surface area of pentagonal trapezohedron given surface-to-volume ratio using this online calculator? To use this online calculator for Surface area of pentagonal trapezohedron given surface-to-volume ratio, enter surface to volume ratio (r) and hit the calculate button. Here is how the Surface area of pentagonal trapezohedron given surface-to-volume ratio calculation can be explained with given input values -> 722.9211 = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*0.5))^2).

FAQ

What is Surface area of pentagonal trapezohedron given surface-to-volume ratio?
The Surface area of pentagonal trapezohedron given surface-to-volume ratio formula is defined as measure of the total area that the surface of the object occupies of a pentagonal trapezohedron, where a =pentagonal trapezohedron edge and is represented as SA = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*r))^2) or surface_area = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^2). surface to volume ratio is fraction of surface to volume.
How to calculate Surface area of pentagonal trapezohedron given surface-to-volume ratio?
The Surface area of pentagonal trapezohedron given surface-to-volume ratio formula is defined as measure of the total area that the surface of the object occupies of a pentagonal trapezohedron, where a =pentagonal trapezohedron edge is calculated using surface_area = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*surface to volume ratio))^2). To calculate Surface area 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 Surface Area?
In this formula, Surface Area uses surface to volume ratio. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • surface_area = 2*pi*Radius*(2*Radius+Side)
  • surface_area = 6*Side^2
  • surface_area = 2*(Length*Width+Length*Height+Width*Height)
  • surface_area = 4*pi*Radius^2
  • surface_area = 3*(sqrt(25+(10*sqrt(5))))*(Side^2)
  • surface_area = 5*(sqrt(3))*(Side^2)
  • surface_area = 2*(sqrt(3))*(Side^2)
  • surface_area = (sqrt(3))*(Side^2)
  • surface_area = 2*((Length*Height)+(Height*Breadth)+(Length*Breadth))
  • surface_area = (2*Base Area)+(Height*Base Perimeter)
  • surface_area = (Base*Height)+(2*Length*Side)+(Length*Base)
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