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Volume of pentagonal trapezohedron given height Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = (5/12)*(3+sqrt(5))*((Height/((sqrt(5+2*sqrt(5)))))^3)
V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^3)
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
V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^3) --> (5/12)*(3+sqrt(5))*((12/((sqrt(5+2*sqrt(5)))))^3)
Evaluating ... ...
V = 129.320057254921
STEP 3: Convert Result to Output's Unit
129.320057254921 Cubic Meter --> No Conversion Required
FINAL ANSWER
129.320057254921 Cubic Meter <-- Volume
(Calculation completed in 00.000 seconds)

11 Other formulas that you can solve using the same Inputs

Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Total Surface Area of a Cone
total_surface_area = pi*Radius*(Radius+sqrt(Radius^2+Height^2)) Go
Lateral Surface Area of a Cone
lateral_surface_area = pi*Radius*sqrt(Radius^2+Height^2) Go
Total Surface Area of a Cylinder
total_surface_area = 2*pi*Radius*(Height+Radius) Go
Lateral Surface Area of a Cylinder
lateral_surface_area = 2*pi*Radius*Height Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
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

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 height Formula

volume = (5/12)*(3+sqrt(5))*((Height/((sqrt(5+2*sqrt(5)))))^3)
V = (5/12)*(3+sqrt(5))*((h/((sqrt(5+2*sqrt(5)))))^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 height?

Volume of pentagonal trapezohedron given height calculator uses volume = (5/12)*(3+sqrt(5))*((Height/((sqrt(5+2*sqrt(5)))))^3) to calculate the Volume, The Volume of pentagonal trapezohedron given height 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 height using this online calculator? To use this online calculator for Volume of pentagonal trapezohedron given height, enter Height (h) and hit the calculate button. Here is how the Volume of pentagonal trapezohedron given height calculation can be explained with given input values -> 129.3201 = (5/12)*(3+sqrt(5))*((12/((sqrt(5+2*sqrt(5)))))^3).

FAQ

What is Volume of pentagonal trapezohedron given height?
The Volume of pentagonal trapezohedron given height 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))*((h/((sqrt(5+2*sqrt(5)))))^3) or volume = (5/12)*(3+sqrt(5))*((Height/((sqrt(5+2*sqrt(5)))))^3). Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Volume of pentagonal trapezohedron given height?
The Volume of pentagonal trapezohedron given height 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))*((Height/((sqrt(5+2*sqrt(5)))))^3). To calculate Volume of pentagonal trapezohedron given height, 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 Volume?
In this formula, Volume uses Height. 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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