Midsphere Radius of Rhombicosidodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
rm = sqrt(10+(4*sqrt(5)))/2*sqrt(TSA/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
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
Midsphere Radius of Rhombicosidodecahedron - (Measured in Meter) - Midsphere Radius of Rhombicosidodecahedron is the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere.
Total Surface Area of Rhombicosidodecahedron - (Measured in Square Meter) - Total Surface Area of Rhombicosidodecahedron is the total quantity of plane enclosed by the entire surface of the of the Rhombicosidodecahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Rhombicosidodecahedron: 5900 Square Meter --> 5900 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(10+(4*sqrt(5)))/2*sqrt(TSA/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) --> sqrt(10+(4*sqrt(5)))/2*sqrt(5900/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Evaluating ... ...
rm = 21.7062957313128
STEP 3: Convert Result to Output's Unit
21.7062957313128 Meter --> No Conversion Required
FINAL ANSWER
21.7062957313128 21.7063 Meter <-- Midsphere Radius of Rhombicosidodecahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verified by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has verified this Calculator and 1700+ more calculators!

5 Midsphere Radius of Rhombicosidodecahedron Calculators

Midsphere Radius of Rhombicosidodecahedron given Surface to Volume Ratio
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5))))
Midsphere Radius of Rhombicosidodecahedron given Total Surface Area
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Midsphere Radius of Rhombicosidodecahedron given Circumsphere Radius
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))*Circumsphere Radius of Rhombicosidodecahedron/(sqrt(11+(4*sqrt(5))))
Midsphere Radius of Rhombicosidodecahedron given Volume
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(1/3)
Midsphere Radius of Rhombicosidodecahedron
Go Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron

Midsphere Radius of Rhombicosidodecahedron given Total Surface Area Formula

Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
rm = sqrt(10+(4*sqrt(5)))/2*sqrt(TSA/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

What is a Rhombicosidodecahedron?

In geometry, the Rhombicosidodecahedron, is an Archimedean solid, one of the 13 convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges. If you expand an icosahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and do the same to its dual dodecahedron, and patch the square holes in the result, you get a Rhombicosidodecahedron. Therefore, it has the same number of triangles as an icosahedron and the same number of pentagons as a dodecahedron, with a square for each edge of either.

How to Calculate Midsphere Radius of Rhombicosidodecahedron given Total Surface Area?

Midsphere Radius of Rhombicosidodecahedron given Total Surface Area calculator uses Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) to calculate the Midsphere Radius of Rhombicosidodecahedron, Midsphere Radius of Rhombicosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Rhombicosidodecahedron. Midsphere Radius of Rhombicosidodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Rhombicosidodecahedron given Total Surface Area using this online calculator? To use this online calculator for Midsphere Radius of Rhombicosidodecahedron given Total Surface Area, enter Total Surface Area of Rhombicosidodecahedron (TSA) and hit the calculate button. Here is how the Midsphere Radius of Rhombicosidodecahedron given Total Surface Area calculation can be explained with given input values -> 21.7063 = sqrt(10+(4*sqrt(5)))/2*sqrt(5900/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))).

FAQ

What is Midsphere Radius of Rhombicosidodecahedron given Total Surface Area?
Midsphere Radius of Rhombicosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Rhombicosidodecahedron and is represented as rm = sqrt(10+(4*sqrt(5)))/2*sqrt(TSA/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))) or Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))). Total Surface Area of Rhombicosidodecahedron is the total quantity of plane enclosed by the entire surface of the of the Rhombicosidodecahedron.
How to calculate Midsphere Radius of Rhombicosidodecahedron given Total Surface Area?
Midsphere Radius of Rhombicosidodecahedron given Total Surface Area formula is defined as the radius of the sphere for which all the edges of the Rhombicosidodecahedron become a tangent line on that sphere, and calculated using the total surface area of the Rhombicosidodecahedron is calculated using Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*sqrt(Total Surface Area of Rhombicosidodecahedron/(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))). To calculate Midsphere Radius of Rhombicosidodecahedron given Total Surface Area, you need Total Surface Area of Rhombicosidodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Rhombicosidodecahedron 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 Midsphere Radius of Rhombicosidodecahedron?
In this formula, Midsphere Radius of Rhombicosidodecahedron uses Total Surface Area of Rhombicosidodecahedron. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*Edge Length of Rhombicosidodecahedron
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*((3*Volume of Rhombicosidodecahedron)/(60+(29*sqrt(5))))^(1/3)
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))*Circumsphere Radius of Rhombicosidodecahedron/(sqrt(11+(4*sqrt(5))))
  • Midsphere Radius of Rhombicosidodecahedron = sqrt(10+(4*sqrt(5)))/2*(3*(30+(5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Rhombicosidodecahedron*(60+(29*sqrt(5))))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!