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Volume of Dodecahedron given Total Surface Area Formula

GoVolume of Dodecahedron Formula

GoVolume of Dodecahedron given Space Diagonal Formula

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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{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

V - Volume of Dodecahedron?TSA - Total Surface Area of Dodecahedron?

Volume of Dodecahedron given Total Surface Area Example

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Here is how the Volume of Dodecahedron given Total Surface Area equation looks like with Values.

Here is how the Volume of Dodecahedron given Total Surface Area equation looks like with Units.

Here is how the Volume of Dodecahedron given Total Surface Area equation looks like.

7861.2061 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

7861.2061m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2100m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

7861.2061 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

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Volume of Dodecahedron given Total Surface Area Solution

Follow our step by step solution on how to calculate Volume of Dodecahedron given Total Surface Area?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2100m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

Next Step Evaluate

∴

V = 7861.2060929223m³

LAST Step Rounding Answer

∴

V = 7861.2061m³

Volume of Dodecahedron given Total Surface Area 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

Total Surface Area of Dodecahedron

Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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 Space Diagonal

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{3}

Go Volume of Dodecahedron given Circumsphere Radius

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

Go Volume of Dodecahedron given Face Area

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

How to Evaluate Volume of Dodecahedron given Total Surface Area?

Volume of Dodecahedron given Total Surface Area evaluator uses Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2) to evaluate the Volume of Dodecahedron, The Volume of Dodecahedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Dodecahedron, and calculated using the total surface area of Dodecahedron. Volume of Dodecahedron is denoted by V symbol.

How to evaluate Volume of Dodecahedron given Total Surface Area using this online evaluator? To use this online evaluator for Volume of Dodecahedron given Total Surface Area, enter Total Surface Area of Dodecahedron (TSA) and hit the calculate button.

FAQs on Volume of Dodecahedron given Total Surface Area

What is the formula to find Volume of Dodecahedron given Total Surface Area?

The formula of Volume of Dodecahedron given Total Surface Area is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2). Here is an example- 7861.206 = 1/4*(15+(7*sqrt(5)))*(2100/(3*sqrt(25+(10*sqrt(5)))))^(3/2).

How to calculate Volume of Dodecahedron given Total Surface Area?

With Total Surface Area of Dodecahedron (TSA) we can find Volume of Dodecahedron given Total Surface Area using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))^(3/2). 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*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3

Can the Volume of Dodecahedron given Total Surface Area be negative?

No, the Volume of Dodecahedron given Total Surface Area, measured in Volume cannot be negative.

Which unit is used to measure Volume of Dodecahedron given Total Surface Area?

Volume of Dodecahedron given Total Surface Area 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 Total Surface Area can be measured.

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