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Circumradius of Regular Polygon given Inradius Formula

GoCircumradius of Regular Polygon Formula

GoCircumradius of Regular Polygon given Perimeter Formula

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The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices. Check FAQs

r c = \frac{r i}{\cos (\frac{π}{N S})}

r_c - Circumradius of Regular Polygon?r_i - Inradius of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Circumradius of Regular Polygon given Inradius Example

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Here is how the Circumradius of Regular Polygon given Inradius equation looks like with Values.

Here is how the Circumradius of Regular Polygon given Inradius equation looks like with Units.

Here is how the Circumradius of Regular Polygon given Inradius equation looks like.

12.9887 = \frac{12}{\cos (\frac{3.1416}{8})}

12.9887m = \frac{12m}{\cos (\frac{3.1416}{8})}

12.9887 = \frac{12}{\cos (\frac{3.1416}{8})}

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Circumradius of Regular Polygon given Inradius Solution

Follow our step by step solution on how to calculate Circumradius of Regular Polygon given Inradius?

FIRST Step Consider the formula

r c = \frac{r i}{\cos (\frac{π}{N S})}

Next Step Substitute values of Variables

∴

r c = \frac{12m}{\cos (\frac{π}{8})}

Next Step Substitute values of Constants

∴

r c = \frac{12m}{\cos (\frac{3.1416}{8})}

Next Step Prepare to Evaluate

∴

r c = \frac{12}{\cos (\frac{3.1416}{8})}

Next Step Evaluate

∴

r c = 12.9887064035087m

LAST Step Rounding Answer

∴

r c = 12.9887m

Circumradius of Regular Polygon given Inradius Formula Elements

Variables

Constants

Functions

Circumradius of Regular Polygon

The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Regular Polygon

Inradius of Regular Polygon

Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Regular Polygon

Number of Sides of Regular Polygon

The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.

Symbol: N_S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Sides of Regular Polygon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Circumradius of Regular Polygon

Go Circumradius of Regular Polygon

r c = \frac{l e}{2 \cdot \sin (\frac{π}{N S})}

Go Circumradius of Regular Polygon given Perimeter

r c = \frac{P}{2 \cdot N S \cdot \sin (\frac{π}{N S})}

Go Circumradius of Regular Polygon given Area

r c = \sqrt{\frac{2 \cdot A}{N S \cdot \sin (\frac{2 \cdot π}{N S})}}

How to Evaluate Circumradius of Regular Polygon given Inradius?

Circumradius of Regular Polygon given Inradius evaluator uses Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon) to evaluate the Circumradius of Regular Polygon, Circumradius of Regular Polygon given Inradius formula can be defined as the radius of a circumcircle touching each of the Regular Polygon's vertices, calculated using its inradius. Circumradius of Regular Polygon is denoted by r_c symbol.

How to evaluate Circumradius of Regular Polygon given Inradius using this online evaluator? To use this online evaluator for Circumradius of Regular Polygon given Inradius, enter Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S) and hit the calculate button.

FAQs on Circumradius of Regular Polygon given Inradius

What is the formula to find Circumradius of Regular Polygon given Inradius?

The formula of Circumradius of Regular Polygon given Inradius is expressed as Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon). Here is an example- 12.98871 = 12/cos(pi/8).

How to calculate Circumradius of Regular Polygon given Inradius?

With Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S) we can find Circumradius of Regular Polygon given Inradius using the formula - Circumradius of Regular Polygon = Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon). This formula also uses Archimedes' constant and Cosine function(s).

What are the other ways to Calculate Circumradius of Regular Polygon?

Here are the different ways to Calculate Circumradius of Regular Polygon-

Circumradius of Regular Polygon=Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon))
Circumradius of Regular Polygon=Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon))
Circumradius of Regular Polygon=sqrt((2*Area of Regular Polygon)/(Number of Sides of Regular Polygon*sin((2*pi)/Number of Sides of Regular Polygon)))

Can the Circumradius of Regular Polygon given Inradius be negative?

No, the Circumradius of Regular Polygon given Inradius, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Regular Polygon given Inradius?

Circumradius of Regular Polygon given Inradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Regular Polygon given Inradius can be measured.

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Circumradius of Regular Polygon given Inradius Formula

​GoCircumradius of Regular Polygon Formula

​GoCircumradius of Regular Polygon given Perimeter Formula

Circumradius of Regular Polygon given Inradius Example

Circumradius of Regular Polygon given Inradius Solution

Circumradius of Regular Polygon given Inradius Formula Elements

Other Formulas to find Circumradius of Regular Polygon

How to Evaluate Circumradius of Regular Polygon given Inradius?

FAQs on Circumradius of Regular Polygon given Inradius

Variable Name

GoCircumradius of Regular Polygon Formula

GoCircumradius of Regular Polygon given Perimeter Formula