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Circumradius of Pentagon given Inradius Formula

GoCircumradius of Pentagon given Edge Length using Central Angle Formula

GoCircumradius of Pentagon Formula

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The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon. Check FAQs

r c = \frac{r i}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

r_c - Circumradius of Pentagon?r_i - Inradius of Pentagon?

Circumradius of Pentagon given Inradius Example

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

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

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

8.6525 = \frac{7}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

8.6525m = \frac{7m}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

8.6525 = \frac{7}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

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Circumradius of Pentagon given Inradius Solution

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

FIRST Step Consider the formula

r c = \frac{r i}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

r c = \frac{7m}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

r c = \frac{7}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

r c = 8.65247584249853m

LAST Step Rounding Answer

∴

r c = 8.6525m

Circumradius of Pentagon given Inradius Formula Elements

Variables

Functions

Circumradius of Pentagon

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Pentagon

Inradius of Pentagon

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

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.

Syntax: sqrt(Number)

Other Formulas to find Circumradius of Pentagon

Go Circumradius of Pentagon given Edge Length using Central Angle

r c = \frac{l e}{2 \cdot \sin (\frac{π}{5})}

Go Circumradius of Pentagon

r c = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

Go Circumradius of Pentagon given Inradius using Central Angle

r c = \frac{r i}{\cos (\frac{π}{5})}

Go Circumradius of Pentagon given Height and Inradius

r c = h - r i

How to Evaluate Circumradius of Pentagon given Inradius?

Circumradius of Pentagon given Inradius evaluator uses Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))) to evaluate the Circumradius of Pentagon, Circumradius of Pentagon given Inradius is defined as the length of the line joining the center and one point on the circumcircle of the Pentagon, calculated using inradius. Circumradius of Pentagon is denoted by r_c symbol.

How to evaluate Circumradius of Pentagon given Inradius using this online evaluator? To use this online evaluator for Circumradius of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button.

FAQs on Circumradius of Pentagon given Inradius

What is the formula to find Circumradius of Pentagon given Inradius?

The formula of Circumradius of Pentagon given Inradius is expressed as Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))). Here is an example- 8.652476 = (7)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))).

How to calculate Circumradius of Pentagon given Inradius?

With Inradius of Pentagon (r_i) we can find Circumradius of Pentagon given Inradius using the formula - Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Pentagon?

Here are the different ways to Calculate Circumradius of Pentagon-

Circumradius of Pentagon=(Edge Length of Pentagon)/(2*sin(pi/5))
Circumradius of Pentagon=Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
Circumradius of Pentagon=Inradius of Pentagon/(cos(pi/5))

Can the Circumradius of Pentagon given Inradius be negative?

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

Which unit is used to measure Circumradius of Pentagon given Inradius?

Circumradius of Pentagon 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 Pentagon given Inradius can be measured.

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