Insphere Radius of Dodecahedron given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2
ri = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*LSA)/(5*sqrt(25+(10*sqrt(5)))))/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
Insphere Radius of Dodecahedron - (Measured in Meter) - Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
Lateral Surface Area of Dodecahedron - (Measured in Square Meter) - Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Lateral Surface Area of Dodecahedron: 1750 Square Meter --> 1750 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*LSA)/(5*sqrt(25+(10*sqrt(5)))))/2 --> sqrt((25+(11*sqrt(5)))/10)*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5)))))/2
Evaluating ... ...
ri = 11.2302944184604
STEP 3: Convert Result to Output's Unit
11.2302944184604 Meter --> No Conversion Required
FINAL ANSWER
11.2302944184604 11.23029 Meter <-- Insphere Radius of Dodecahedron
(Calculation completed in 00.004 seconds)

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Insphere Radius of Dodecahedron Calculators

Insphere Radius of Dodecahedron given Total Surface Area
​ LaTeX ​ Go Insphere Radius of Dodecahedron = sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))
Insphere Radius of Dodecahedron given Face Area
​ LaTeX ​ Go Insphere Radius of Dodecahedron = sqrt((Face Area of Dodecahedron*(25+(11*sqrt(5))))/(10*sqrt(25+(10*sqrt(5)))))
Insphere Radius of Dodecahedron given Volume
​ LaTeX ​ Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron
​ LaTeX ​ Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2

Insphere Radius of Dodecahedron given Lateral Surface Area Formula

​LaTeX ​Go
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2
ri = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*LSA)/(5*sqrt(25+(10*sqrt(5)))))/2

What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

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 Insphere Radius of Dodecahedron given Lateral Surface Area?

Insphere Radius of Dodecahedron given Lateral Surface Area calculator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2 to calculate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Lateral Surface Area formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using lateral surface area of Dodecahedron. Insphere Radius of Dodecahedron is denoted by ri symbol.

How to calculate Insphere Radius of Dodecahedron given Lateral Surface Area using this online calculator? To use this online calculator for Insphere Radius of Dodecahedron given Lateral Surface Area, enter Lateral Surface Area of Dodecahedron (LSA) and hit the calculate button. Here is how the Insphere Radius of Dodecahedron given Lateral Surface Area calculation can be explained with given input values -> 11.23029 = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5)))))/2.

FAQ

What is Insphere Radius of Dodecahedron given Lateral Surface Area?
The Insphere Radius of Dodecahedron given Lateral Surface Area formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using lateral surface area of Dodecahedron and is represented as ri = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*LSA)/(5*sqrt(25+(10*sqrt(5)))))/2 or Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2. Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.
How to calculate Insphere Radius of Dodecahedron given Lateral Surface Area?
The Insphere Radius of Dodecahedron given Lateral Surface Area formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using lateral surface area of Dodecahedron is calculated using Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))/2. To calculate Insphere Radius of Dodecahedron given Lateral Surface Area, you need Lateral Surface Area of Dodecahedron (LSA). With our tool, you need to enter the respective value for Lateral Surface Area of Dodecahedron 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 Insphere Radius of Dodecahedron?
In this formula, Insphere Radius of Dodecahedron uses Lateral Surface Area of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
  • Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
  • Insphere Radius of Dodecahedron = sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))
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