Volume of Icosahedron given Total Surface Area Calculator

✖Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.ⓘ Total Surface Area of Icosahedron [TSA]

+10%

-10%

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

⎘ Copy

👎

Formula

✖

Volume of Icosahedron given Total Surface Area

Formula

`"V" = (3+sqrt(5))/(12*sqrt(5))*("TSA"/sqrt(3))^(3/2)`

Example

`"2196.731m³"=(3+sqrt(5))/(12*sqrt(5))*("870m²"/sqrt(3))^(3/2)`

Calculator

LaTeX

Reset

👍

Download Icosahedron Formula PDF

Volume of Icosahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)
V = (3+sqrt(5))/(12*sqrt(5))*(TSA/sqrt(3))^(3/2)
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 Icosahedron - (Measured in Cubic Meter) - Volume of Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Icosahedron.
Total Surface Area of Icosahedron - (Measured in Square Meter) - Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Icosahedron: 870 Square Meter --> 870 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (3+sqrt(5))/(12*sqrt(5))*(TSA/sqrt(3))^(3/2) --> (3+sqrt(5))/(12*sqrt(5))*(870/sqrt(3))^(3/2)

Evaluating ... ...

V = 2196.7314403308

STEP 3: Convert Result to Output's Unit

2196.7314403308 Cubic Meter --> No Conversion Required

FINAL ANSWER

2196.7314403308 ≈ 2196.731 Cubic Meter <-- Volume of Icosahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Platonic Solids » Icosahedron » Volume of Icosahedron » Volume of Icosahedron given Total Surface Area

Credits

Created by Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has created this Calculator and 600+ more calculators!

Verified by Manjiri

G.V. Acharya Institute Of Engineering & Technology (GVAIET), Mumbai

Manjiri has verified this Calculator and 10+ more calculators!

< 11 Volume of Icosahedron Calculators

Volume of Icosahedron given Surface to Volume Ratio

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3

Volume of Icosahedron given Circumsphere Radius

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Insphere Radius

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Icosahedron given Space Diagonal

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Total Surface Area

Go Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Volume of Icosahedron given Lateral Surface Area

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2)

Volume of Icosahedron given Midsphere Radius

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^3

Volume of Icosahedron given Face Area

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2)

Volume of Icosahedron given Face Perimeter

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3

Volume of Icosahedron given Perimeter

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*(Perimeter of Icosahedron/30)^3

Volume of Icosahedron

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3

< 4 Volume of Icosahedron Calculators

Volume of Icosahedron given Circumsphere Radius

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Insphere Radius

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Icosahedron given Total Surface Area

Go Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Volume of Icosahedron

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3

Volume of Icosahedron given Total Surface Area Formula

Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)
V = (3+sqrt(5))/(12*sqrt(5))*(TSA/sqrt(3))^(3/2)

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Volume of Icosahedron given Total Surface Area?

Volume of Icosahedron given Total Surface Area calculator uses Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2) to calculate the Volume of Icosahedron, Volume of Icosahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the total surface area of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

How to calculate Volume of Icosahedron given Total Surface Area using this online calculator? To use this online calculator for Volume of Icosahedron given Total Surface Area, enter Total Surface Area of Icosahedron (TSA) and hit the calculate button. Here is how the Volume of Icosahedron given Total Surface Area calculation can be explained with given input values -> 2196.731 = (3+sqrt(5))/(12*sqrt(5))*(870/sqrt(3))^(3/2).

FAQ

What is Volume of Icosahedron given Total Surface Area?

Volume of Icosahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the total surface area of the Icosahedron and is represented as V = (3+sqrt(5))/(12*sqrt(5))*(TSA/sqrt(3))^(3/2) or Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2). Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.

How to calculate Volume of Icosahedron given Total Surface Area?

Volume of Icosahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the total surface area of the Icosahedron is calculated using Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2). To calculate Volume of Icosahedron given Total Surface Area, you need Total Surface Area of Icosahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Icosahedron 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 Icosahedron?

In this formula, Volume of Icosahedron uses Total Surface Area of Icosahedron. We can use 13 other way(s) to calculate the same, which is/are as follows -

Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2)
Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2)
Volume of Icosahedron = 5/12*(3+sqrt(5))*(Perimeter of Icosahedron/30)^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Home

FREE PDFs

🔍 Search