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Volume of pentagonal trapezohedron given long edge Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = (5/12)*(3+sqrt(5))*((Side B/(((sqrt(5)+1)/2)))^3)
V = (5/12)*(3+sqrt(5))*((b/(((sqrt(5)+1)/2)))^3)
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Side B - Side B is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Side B: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = (5/12)*(3+sqrt(5))*((b/(((sqrt(5)+1)/2)))^3) --> (5/12)*(3+sqrt(5))*((7/(((sqrt(5)+1)/2)))^3)
Evaluating ... ...
V = 176.654715117678
STEP 3: Convert Result to Output's Unit
176.654715117678 Cubic Meter --> No Conversion Required
FINAL ANSWER
176.654715117678 Cubic Meter <-- Volume
(Calculation completed in 00.000 seconds)

11 Other formulas that you can solve using the same Inputs

Area of a Triangle when sides are given
area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4 Go
Radius of Inscribed Circle
radius_of_inscribed_circle = sqrt((Semiperimeter Of Triangle -Side A)*(Semiperimeter Of Triangle -Side B)*(Semiperimeter Of Triangle -Side C)/Semiperimeter Of Triangle ) Go
Area of Triangle when semiperimeter is given
area_of_triangle = sqrt(Semiperimeter Of Triangle *(Semiperimeter Of Triangle -Side A)*(Semiperimeter Of Triangle -Side B)*(Semiperimeter Of Triangle -Side C)) Go
Side a of a triangle
side_a = sqrt((Side B)^2+(Side C)^2-2*Side B*Side C*cos(Angle A)) Go
side c of a triangle
side_c = sqrt(Side B^2+Side A^2-2*Side A*Side B*cos(Angle C)) Go
Perimeter of a Right Angled Triangle
perimeter = Side A+Side B+sqrt(Side A^2+Side B^2) Go
Radius of circumscribed circle
radius_of_circumscribed_circle = (Side A*Side B*Side C)/(4*Area Of Triangle) Go
Perimeter of Triangle
perimeter_of_triangle = Side A+Side B+Side C Go
Perimeter of a Parallelogram
perimeter = 2*Side A+2*Side B Go
Perimeter of a Kite
perimeter = 2*(Side A+Side B) Go
Perimeter of an Isosceles Triangle
perimeter = Side A+2*Side B 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 long edge Formula

volume = (5/12)*(3+sqrt(5))*((Side B/(((sqrt(5)+1)/2)))^3)
V = (5/12)*(3+sqrt(5))*((b/(((sqrt(5)+1)/2)))^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 long edge?

Volume of pentagonal trapezohedron given long edge calculator uses volume = (5/12)*(3+sqrt(5))*((Side B/(((sqrt(5)+1)/2)))^3) to calculate the Volume, The Volume of pentagonal trapezohedron given long edge 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 long edge using this online calculator? To use this online calculator for Volume of pentagonal trapezohedron given long edge, enter Side B (b) and hit the calculate button. Here is how the Volume of pentagonal trapezohedron given long edge calculation can be explained with given input values -> 176.6547 = (5/12)*(3+sqrt(5))*((7/(((sqrt(5)+1)/2)))^3).

FAQ

What is Volume of pentagonal trapezohedron given long edge?
The Volume of pentagonal trapezohedron given long edge 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))*((b/(((sqrt(5)+1)/2)))^3) or volume = (5/12)*(3+sqrt(5))*((Side B/(((sqrt(5)+1)/2)))^3). Side B is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Volume of pentagonal trapezohedron given long edge?
The Volume of pentagonal trapezohedron given long edge 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))*((Side B/(((sqrt(5)+1)/2)))^3). To calculate Volume of pentagonal trapezohedron given long edge, you need Side B (b). With our tool, you need to enter the respective value for Side B 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 Side B. 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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