Volume of Pentagonal Hexecontahedron given Total Surface Area Calculator

✖Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.ⓘ Total Surface Area of Pentagonal Hexecontahedron [TSA]

+10%

-10%

✖Volume of Pentagonal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron.ⓘ Volume of Pentagonal Hexecontahedron given Total Surface Area [V]

⎘ Copy

👎

Formula

✖

Volume of Pentagonal Hexecontahedron given Total Surface Area

Formula

`"V" = 5*(("TSA"*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))`

Example

`"12124.27m³"=5*(("2600m²"*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Volume of Pentagonal Hexecontahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
V = 5*((TSA*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Volume of Pentagonal Hexecontahedron - (Measured in Cubic Meter) - Volume of Pentagonal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron.
Total Surface Area of Pentagonal Hexecontahedron - (Measured in Square Meter) - Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Pentagonal Hexecontahedron: 2600 Square Meter --> 2600 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5*((TSA*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) --> 5*((2600*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Evaluating ... ...

V = 12124.2702409322

STEP 3: Convert Result to Output's Unit

12124.2702409322 Cubic Meter --> No Conversion Required

FINAL ANSWER

12124.2702409322 ≈ 12124.27 Cubic Meter <-- Volume of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Pentagonal Hexecontahedron » Volume of Pentagonal Hexecontahedron » Volume of Pentagonal Hexecontahedron given Total Surface Area

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1800+ more calculators!

< 6 Volume of Pentagonal Hexecontahedron Calculators

Volume of Pentagonal Hexecontahedron given Long Edge

Go Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron given Total Surface Area

Go Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron given Insphere Radius

Go Volume of Pentagonal Hexecontahedron = 5*((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron given Midsphere Radius

Go Volume of Pentagonal Hexecontahedron = 5*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

Go Volume of Pentagonal Hexecontahedron = 5*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron

Go Volume of Pentagonal Hexecontahedron = 5*Short Edge of Pentagonal Hexecontahedron^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Volume of Pentagonal Hexecontahedron given Total Surface Area Formula

What is Pentagonal Hexecontahedron?

In geometry, a Pentagonal Hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 60 faces, 150 edges, 92 vertices. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.

How to Calculate Volume of Pentagonal Hexecontahedron given Total Surface Area?

Volume of Pentagonal Hexecontahedron given Total Surface Area calculator uses Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) to calculate the Volume of Pentagonal Hexecontahedron, Volume of Pentagonal Hexecontahedron given Total Surface Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron, calculated using total surface area of Pentagonal Hexecontahedron. Volume of Pentagonal Hexecontahedron is denoted by V symbol.

How to calculate Volume of Pentagonal Hexecontahedron given Total Surface Area using this online calculator? To use this online calculator for Volume of Pentagonal Hexecontahedron given Total Surface Area, enter Total Surface Area of Pentagonal Hexecontahedron (TSA) and hit the calculate button. Here is how the Volume of Pentagonal Hexecontahedron given Total Surface Area calculation can be explained with given input values -> 12124.27 = 5*((2600*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)).

FAQ

What is Volume of Pentagonal Hexecontahedron given Total Surface Area?

Volume of Pentagonal Hexecontahedron given Total Surface Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron, calculated using total surface area of Pentagonal Hexecontahedron and is represented as V = 5*((TSA*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)) or Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)). Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.

How to calculate Volume of Pentagonal Hexecontahedron given Total Surface Area?

Volume of Pentagonal Hexecontahedron given Total Surface Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron, calculated using total surface area of Pentagonal Hexecontahedron is calculated using Volume of Pentagonal Hexecontahedron = 5*((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))^(3/2)*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)). To calculate Volume of Pentagonal Hexecontahedron given Total Surface Area, you need Total Surface Area of Pentagonal Hexecontahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Pentagonal Hexecontahedron 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 of Pentagonal Hexecontahedron?

In this formula, Volume of Pentagonal Hexecontahedron uses Total Surface Area of Pentagonal Hexecontahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Volume of Pentagonal Hexecontahedron = 5*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron = 5*Short Edge of Pentagonal Hexecontahedron^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron = 5*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron = 5*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))
Volume of Pentagonal Hexecontahedron = 5*((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))))^3*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))

Home

FREE PDFs

🔍 Search