FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Volume of Dodecahedron given Circumsphere Radius Formula

GoVolume of Dodecahedron Formula

GoVolume of Dodecahedron given Lateral Surface Area Formula

Fx Copy

LaTeX Copy

Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron. Check FAQs

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

V - Volume of Dodecahedron?r_c - Circumsphere Radius of Dodecahedron?

Volume of Dodecahedron given Circumsphere Radius Example

With values

With units

Only example

Here is how the Volume of Dodecahedron given Circumsphere Radius equation looks like with Values.

Here is how the Volume of Dodecahedron given Circumsphere Radius equation looks like with Units.

Here is how the Volume of Dodecahedron given Circumsphere Radius equation looks like.

7642.4896 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

7642.4896m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

7642.4896 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Volume of Dodecahedron given Circumsphere Radius

Volume of Dodecahedron given Circumsphere Radius Solution

Follow our step by step solution on how to calculate Volume of Dodecahedron given Circumsphere Radius?

FIRST Step Consider the formula

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Next Step Evaluate

∴

V = 7642.48964040848m³

LAST Step Rounding Answer

∴

V = 7642.4896m³

Volume of Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Volume of Dodecahedron

Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Dodecahedron

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Dodecahedron

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 Volume of Dodecahedron

Go Volume of Dodecahedron

V = \frac{(15 + (7 \cdot \sqrt{5})) \cdot {l e}^{3}}{4}

Go Volume of Dodecahedron given Lateral Surface Area

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

Go Volume of Dodecahedron given Perimeter

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{P}{30})}^{3}

How to Evaluate Volume of Dodecahedron given Circumsphere Radius?

Volume of Dodecahedron given Circumsphere Radius evaluator uses Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3 to evaluate the Volume of Dodecahedron, The Volume of Dodecahedron given Circumsphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the circumsphere radius of Dodecahedron. Volume of Dodecahedron is denoted by V symbol.

How to evaluate Volume of Dodecahedron given Circumsphere Radius using this online evaluator? To use this online evaluator for Volume of Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Dodecahedron (r_c) and hit the calculate button.

FAQs on Volume of Dodecahedron given Circumsphere Radius

What is the formula to find Volume of Dodecahedron given Circumsphere Radius?

The formula of Volume of Dodecahedron given Circumsphere Radius is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3. Here is an example- 7642.49 = 1/4*(15+(7*sqrt(5)))*((4*14)/(sqrt(3)*(1+sqrt(5))))^3.

How to calculate Volume of Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Dodecahedron (r_c) we can find Volume of Dodecahedron given Circumsphere Radius using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Dodecahedron?

Here are the different ways to Calculate Volume of Dodecahedron-

Volume of Dodecahedron=((15+(7*sqrt(5)))*Edge Length of Dodecahedron^3)/4
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))^(3/2)
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*(Perimeter of Dodecahedron/30)^3

Can the Volume of Dodecahedron given Circumsphere Radius be negative?

No, the Volume of Dodecahedron given Circumsphere Radius, measured in Volume cannot be negative.

Which unit is used to measure Volume of Dodecahedron given Circumsphere Radius?

Volume of Dodecahedron given Circumsphere Radius is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Dodecahedron given Circumsphere Radius can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit