Circumradius of Hexadecagon given Inradius Calculator

✖Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.ⓘ Circumradius of Hexadecagon given Inradius [r_c]

⎘ Copy

👎

Formula

✖

Circumradius of Hexadecagon given Inradius

Formula

`"r"_{"c"} = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*("r"_{"i"}/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))`

Example

`"12.23509m"=sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*("12m"/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))`

Calculator

LaTeX

Reset

👍

Download Hexadecagon Formula PDF

Circumradius of Hexadecagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))
r_c = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(r_i/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/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

Circumradius of Hexadecagon - (Measured in Meter) - Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
Inradius of Hexadecagon - (Measured in Meter) - Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Hexadecagon: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(r_i/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)) --> sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))

Evaluating ... ...

r_c = 12.2350938984998

STEP 3: Convert Result to Output's Unit

12.2350938984998 Meter --> No Conversion Required

FINAL ANSWER

12.2350938984998 ≈ 12.23509 Meter <-- Circumradius of Hexadecagon

(Calculation completed in 00.020 seconds)

You are here -

Home » Math » Geometry » 2D Geometry » Hexadecagon » Radius of Hexadecagon » Circumradius of Hexadecagon » Circumradius of Hexadecagon given Inradius

Credits

Created by Himanshu Srivastava

Lloyd Business School (LBS), Greater Noida

Himanshu Srivastava has created this Calculator and 100+ more calculators!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Calculator and 1400+ more calculators!

< 12 Circumradius of Hexadecagon Calculators

Circumradius of Hexadecagon given Diagonal across Seven Sides

Go Circumradius of Hexadecagon = (Diagonal across Seven Sides of Hexadecagon*sin(pi/16))/sin((7*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon given Diagonal across Three Sides

Go Circumradius of Hexadecagon = (Diagonal across Three Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon given Diagonal across Five Sides

Go Circumradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon given Diagonal across Six Sides

Go Circumradius of Hexadecagon = (Diagonal across Six Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon given Diagonal across Two Sides

Go Circumradius of Hexadecagon = (Diagonal across Two Sides of Hexadecagon*sin(pi/16))/sin(pi/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon given Height

Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Height of Hexadecagon*sin(pi/16))/sin((7*pi)/16)

Circumradius of Hexadecagon given Diagonal across Four Sides

Go Circumradius of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon given Inradius

Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))

Circumradius of Hexadecagon given Area

Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16)))

Circumradius of Hexadecagon given Perimeter

Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Perimeter of Hexadecagon/16

Circumradius of Hexadecagon

Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Side of Hexadecagon

Circumradius of Hexadecagon given Diagonal across Eight Sides

Go Circumradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon/2

Circumradius of Hexadecagon given Inradius Formula

What is Hexadecagon?

A Hexadecagon is a 16-sided polygon, in which all angles are equal and all sides are congruent. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees. Hexadecagons are sometimes used in art and architecture.

How to Calculate Circumradius of Hexadecagon given Inradius?

Circumradius of Hexadecagon given Inradius calculator uses Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)) to calculate the Circumradius of Hexadecagon, The Circumradius of Hexadecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circle that touches all the vertices of Hexadecagon, calculated using inradius. Circumradius of Hexadecagon is denoted by r_c symbol.

How to calculate Circumradius of Hexadecagon given Inradius using this online calculator? To use this online calculator for Circumradius of Hexadecagon given Inradius, enter Inradius of Hexadecagon (r_i) and hit the calculate button. Here is how the Circumradius of Hexadecagon given Inradius calculation can be explained with given input values -> 12.23509 = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)).

FAQ

What is Circumradius of Hexadecagon given Inradius?

The Circumradius of Hexadecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circle that touches all the vertices of Hexadecagon, calculated using inradius and is represented as r_c = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(r_i/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)) or Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)). Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

How to calculate Circumradius of Hexadecagon given Inradius?

The Circumradius of Hexadecagon given Inradius formula is defined as the straight line connecting the circumcenter and any point on the circle that touches all the vertices of Hexadecagon, calculated using inradius is calculated using Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)). To calculate Circumradius of Hexadecagon given Inradius, you need Inradius of Hexadecagon (r_i). With our tool, you need to enter the respective value for Inradius of Hexadecagon 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 Circumradius of Hexadecagon?

In this formula, Circumradius of Hexadecagon uses Inradius of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -

Circumradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon/2
Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Side of Hexadecagon
Circumradius of Hexadecagon = (Diagonal across Seven Sides of Hexadecagon*sin(pi/16))/sin((7*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon = (Diagonal across Six Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon = (Diagonal across Three Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon = (Diagonal across Two Sides of Hexadecagon*sin(pi/16))/sin(pi/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16)))
Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Perimeter of Hexadecagon/16
Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Height of Hexadecagon*sin(pi/16))/sin((7*pi)/16)

Home

FREE PDFs

🔍 Search