Total Surface Area of Great Icosahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.ⓘ Surface to Volume Ratio of Great Icosahedron [R_A/V]

+10%

-10%

✖Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.ⓘ Total Surface Area of Great Icosahedron given Surface to Volume Ratio [TSA]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

Total Surface Area of Great Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^2
TSA = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V))^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

Total Surface Area of Great Icosahedron - (Measured in Square Meter) - Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.
Surface to Volume Ratio of Great Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Great Icosahedron: 0.6 1 per Meter --> 0.6 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V))^2 --> 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6))^2

Evaluating ... ...

TSA = 8302.78322352339

STEP 3: Convert Result to Output's Unit

8302.78322352339 Square Meter --> No Conversion Required

FINAL ANSWER

8302.78322352339 ≈ 8302.783 Square Meter <-- Total Surface Area of Great Icosahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Great Icosahedron » Surface Area of Great Icosahedron » Total Surface Area of Great Icosahedron » Total Surface Area of Great Icosahedron given Surface to Volume Ratio

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< Total Surface Area of Great Icosahedron Calculators

Total Surface Area of Great Icosahedron given Long Ridge Length

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2

Total Surface Area of Great Icosahedron given Mid Ridge Length

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^2

Total Surface Area of Great Icosahedron given Short Ridge Length

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((5*Short Ridge Length of Great Icosahedron)/sqrt(10))^2

Total Surface Area of Great Icosahedron

LaTeX Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*Edge Length of Great Icosahedron^2

Total Surface Area of Great Icosahedron given Surface to Volume Ratio Formula

LaTeX Go

What is Great Icosahedron?

The Great Icosahedron can be constructed from an icosahedron with unit edge lengths by taking the 20 sets of vertices that are mutually spaced by a distance phi, the golden ratio. The solid therefore consists of 20 equilateral triangles. The symmetry of their arrangement is such that the resulting solid contains 12 pentagrams.

How to Calculate Total Surface Area of Great Icosahedron given Surface to Volume Ratio?

Total Surface Area of Great Icosahedron given Surface to Volume Ratio calculator uses Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^2 to calculate the Total Surface Area of Great Icosahedron, Total Surface Area of Great Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using surface to volume ratio. Total Surface Area of Great Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area of Great Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Great Icosahedron (R_A/V) and hit the calculate button. Here is how the Total Surface Area of Great Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 8302.783 = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*0.6))^2.

FAQ

What is Total Surface Area of Great Icosahedron given Surface to Volume Ratio?

Total Surface Area of Great Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using surface to volume ratio and is represented as TSA = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*R_A/V))^2 or Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^2. Surface to Volume Ratio of Great Icosahedron is the numerical ratio of the total surface area of a Great Icosahedron to the volume of the Great Icosahedron.

How to calculate Total Surface Area of Great Icosahedron given Surface to Volume Ratio?

Total Surface Area of Great Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using surface to volume ratio is calculated using Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^2. To calculate Total Surface Area of Great Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Great Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Great 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 Total Surface Area of Great Icosahedron?

In this formula, Total Surface Area of Great Icosahedron uses Surface to Volume Ratio of Great Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*Edge Length of Great Icosahedron^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2

Home

FREE PDFs

🔍 Search