Volume of Pentagonal Prism Calculator

✖The Base Edge Length of Pentagonal Prism is the length of the straight line connecting any two adjacent vertices of the base of the Pentagonal Prism.ⓘ Base Edge Length of Pentagonal Prism [l_e(Base)]			+10% -10%
✖The Height of Pentagonal Prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the Pentagonal Prism.ⓘ Height of Pentagonal Prism [h]			+10% -10%

✖The Volume of Pentagonal Prism is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Prism.ⓘ Volume of Pentagonal Prism [V]

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Formula

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Volume of Pentagonal Prism

Formula

`"V" = sqrt(5*(5+(2*sqrt(5))))/4*"l"_{"e(Base)"}^2*"h"`

Example

`"2580.716m³"=sqrt(5*(5+(2*sqrt(5))))/4*("10m")^2*"15m"`

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Volume of Pentagonal Prism Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism
V = sqrt(5*(5+(2*sqrt(5))))/4*l_e(Base)^2*h
This formula uses 1 Functions, 3 Variables

Functions Used

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., sqrt(Number)

Variables Used

Volume of Pentagonal Prism - (Measured in Cubic Meter) - The Volume of Pentagonal Prism is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Prism.
Base Edge Length of Pentagonal Prism - (Measured in Meter) - The Base Edge Length of Pentagonal Prism is the length of the straight line connecting any two adjacent vertices of the base of the Pentagonal Prism.
Height of Pentagonal Prism - (Measured in Meter) - The Height of Pentagonal Prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the Pentagonal Prism.

STEP 1: Convert Input(s) to Base Unit

Base Edge Length of Pentagonal Prism: 10 Meter --> 10 Meter No Conversion Required
Height of Pentagonal Prism: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = sqrt(5*(5+(2*sqrt(5))))/4*l_e(Base)^2*h --> sqrt(5*(5+(2*sqrt(5))))/4*10^2*15

Evaluating ... ...

V = 2580.71610088345

STEP 3: Convert Result to Output's Unit

2580.71610088345 Cubic Meter --> No Conversion Required

FINAL ANSWER

2580.71610088345 ≈ 2580.716 Cubic Meter <-- Volume of Pentagonal Prism

(Calculation completed in 00.020 seconds)

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< 4 Pentagonal Prism Calculators

Total Surface Area of Pentagonal Prism

Go Total Surface Area of Pentagonal Prism = (5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism)+sqrt(5*(5+(2*sqrt(5))))/2*Base Edge Length of Pentagonal Prism^2

Volume of Pentagonal Prism

Go Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism

Base Area of Pentagonal Prism

Go Base Area of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2

Lateral Surface Area of Pentagonal Prism

Go Lateral Surface Area of Pentagonal Prism = 5*Base Edge Length of Pentagonal Prism*Height of Pentagonal Prism

Volume of Pentagonal Prism Formula

Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism
V = sqrt(5*(5+(2*sqrt(5))))/4*l_e(Base)^2*h

What is Pentagonal Prism?

In geometry, the Pentagonal Prism is a prism with pentagonal base. This polyhedron has 7 faces, 15 edges, and 10 vertices.

What is Prism?

In mathematics, a Prism is a polyhedron with two polygonal bases parallel to each other. In physics (optics), a prism is defined as the transparent optical element with flat polished surfaces that refract light. Lateral faces join the two polygonal bases. The lateral faces are mostly rectangular. In some cases, it may be a parallelogram.

How to Calculate Volume of Pentagonal Prism?

Volume of Pentagonal Prism calculator uses Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism to calculate the Volume of Pentagonal Prism, The Volume of Pentagonal Prism formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Prism. Volume of Pentagonal Prism is denoted by V symbol.

How to calculate Volume of Pentagonal Prism using this online calculator? To use this online calculator for Volume of Pentagonal Prism, enter Base Edge Length of Pentagonal Prism (l_e(Base)) & Height of Pentagonal Prism (h) and hit the calculate button. Here is how the Volume of Pentagonal Prism calculation can be explained with given input values -> 2580.716 = sqrt(5*(5+(2*sqrt(5))))/4*10^2*15.

FAQ

What is Volume of Pentagonal Prism?

The Volume of Pentagonal Prism formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Prism and is represented as V = sqrt(5*(5+(2*sqrt(5))))/4*l_e(Base)^2*h or Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism. The Base Edge Length of Pentagonal Prism is the length of the straight line connecting any two adjacent vertices of the base of the Pentagonal Prism & The Height of Pentagonal Prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the Pentagonal Prism.

How to calculate Volume of Pentagonal Prism?

The Volume of Pentagonal Prism formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Prism is calculated using Volume of Pentagonal Prism = sqrt(5*(5+(2*sqrt(5))))/4*Base Edge Length of Pentagonal Prism^2*Height of Pentagonal Prism. To calculate Volume of Pentagonal Prism, you need Base Edge Length of Pentagonal Prism (l_e(Base)) & Height of Pentagonal Prism (h). With our tool, you need to enter the respective value for Base Edge Length of Pentagonal Prism & Height of Pentagonal Prism and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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