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Volume of Dodecahedron given Lateral Surface Area Formula

GoVolume of Dodecahedron Formula

GoVolume of Dodecahedron given Circumsphere Radius 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{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

V - Volume of Dodecahedron?LSA - Lateral Surface Area of Dodecahedron?

Volume of Dodecahedron given Lateral Surface Area Example

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

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

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

7861.2061 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

7861.2061m³ = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

7861.2061 = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}})}^{\frac{3}{2}}

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Volume of Dodecahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

V = \frac{1}{4} \cdot (15 + (7 \cdot \sqrt{5})) \cdot {(\frac{2 \cdot 1750m²}{5 \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{2 \cdot 1750}{5 \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 Lateral 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

Lateral Surface Area of Dodecahedron

Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral 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 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 Perimeter

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

How to Evaluate Volume of Dodecahedron given Lateral Surface Area?

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

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

FAQs on Volume of Dodecahedron given Lateral Surface Area

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

The formula of Volume of Dodecahedron given Lateral Surface Area is expressed as Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))^(3/2). Here is an example- 7861.206 = 1/4*(15+(7*sqrt(5)))*((2*1750)/(5*sqrt(25+(10*sqrt(5)))))^(3/2).

How to calculate Volume of Dodecahedron given Lateral Surface Area?

With Lateral Surface Area of Dodecahedron (LSA) we can find Volume of Dodecahedron given Lateral Surface Area using the formula - Volume of Dodecahedron = 1/4*(15+(7*sqrt(5)))*((2*Lateral Surface Area of Dodecahedron)/(5*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)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^3
Volume of Dodecahedron=1/4*(15+(7*sqrt(5)))*(Perimeter of Dodecahedron/30)^3

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

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

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

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

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