Volume of Rhombohedron given Total Surface Area Calculator

✖Total Surface Area of Rhombohedron is the total quantity of plane enclosed on the entire surface of the Rhombohedron.ⓘ Total Surface Area of Rhombohedron [TSA]			+10% -10%
✖Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.ⓘ Acute Angle of Rhombohedron [∠_Acute]			+10% -10%

✖Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron.ⓘ Volume of Rhombohedron given Total Surface Area [V]

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Formula

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Volume of Rhombohedron given Total Surface Area

Formula

`"V" = (sqrt("TSA"/(6*sin("∠"_{"Acute"}))))^3*(1-cos("∠"_{"Acute"}))*sqrt(1+2*cos("∠"_{"Acute"}))`

Example

`"540.696m³"=(sqrt("460m²"/(6*sin("50°"))))^3*(1-cos("50°"))*sqrt(1+2*cos("50°"))`

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Volume of Rhombohedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rhombohedron = (sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))
V = (sqrt(TSA/(6*sin(∠_Acute))))^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))
This formula uses 3 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
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 Rhombohedron - (Measured in Cubic Meter) - Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron.
Total Surface Area of Rhombohedron - (Measured in Square Meter) - Total Surface Area of Rhombohedron is the total quantity of plane enclosed on the entire surface of the Rhombohedron.
Acute Angle of Rhombohedron - (Measured in Radian) - Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Rhombohedron: 460 Square Meter --> 460 Square Meter No Conversion Required
Acute Angle of Rhombohedron: 50 Degree --> 0.872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (sqrt(TSA/(6*sin(∠_Acute))))^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute)) --> (sqrt(460/(6*sin(0.872664625997001))))^3*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))

Evaluating ... ...

V = 540.696048809246

STEP 3: Convert Result to Output's Unit

540.696048809246 Cubic Meter --> No Conversion Required

FINAL ANSWER

540.696048809246 ≈ 540.696 Cubic Meter <-- Volume of Rhombohedron

(Calculation completed in 00.005 seconds)

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< 4 Volume of Rhombohedron Calculators

Volume of Rhombohedron given Surface to Volume Ratio

Go Volume of Rhombohedron = ((6*sin(Acute Angle of Rhombohedron))/(Surface to Volume Ratio of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))

Volume of Rhombohedron given Total Surface Area

Go Volume of Rhombohedron = (sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))

Volume of Rhombohedron given Obtuse Angle

Go Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron))

Volume of Rhombohedron

Go Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))

Volume of Rhombohedron given Total Surface Area Formula

What is a Rhombohedron?

A Rhombohedron (also called a rhombic hexahedron) is a three-dimensional figure like a cuboid (also called a rectangular parallelepiped), except that its faces are not rectangles but rhombi. It is a special case of a parallelepiped where all edges are the same length. It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. In general, a Rhombohedron can have up to three types of rhombic faces in congruent opposite pairs, Ci symmetry, order 2.

How to Calculate Volume of Rhombohedron given Total Surface Area?

Volume of Rhombohedron given Total Surface Area calculator uses Volume of Rhombohedron = (sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)) to calculate the Volume of Rhombohedron, Volume of Rhombohedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron, calculated using its total surface area. Volume of Rhombohedron is denoted by V symbol.

How to calculate Volume of Rhombohedron given Total Surface Area using this online calculator? To use this online calculator for Volume of Rhombohedron given Total Surface Area, enter Total Surface Area of Rhombohedron (TSA) & Acute Angle of Rhombohedron (∠_Acute) and hit the calculate button. Here is how the Volume of Rhombohedron given Total Surface Area calculation can be explained with given input values -> 540.696 = (sqrt(460/(6*sin(0.872664625997001))))^3*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001)).

FAQ

What is Volume of Rhombohedron given Total Surface Area?

Volume of Rhombohedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron, calculated using its total surface area and is represented as V = (sqrt(TSA/(6*sin(∠_Acute))))^3*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute)) or Volume of Rhombohedron = (sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)). Total Surface Area of Rhombohedron is the total quantity of plane enclosed on the entire surface of the Rhombohedron & Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees.

How to calculate Volume of Rhombohedron given Total Surface Area?

Volume of Rhombohedron given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the surface of the Rhombohedron, calculated using its total surface area is calculated using Volume of Rhombohedron = (sqrt(Total Surface Area of Rhombohedron/(6*sin(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)). To calculate Volume of Rhombohedron given Total Surface Area, you need Total Surface Area of Rhombohedron (TSA) & Acute Angle of Rhombohedron (∠_Acute). With our tool, you need to enter the respective value for Total Surface Area of Rhombohedron & Acute Angle of Rhombohedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Rhombohedron?

In this formula, Volume of Rhombohedron uses Total Surface Area of Rhombohedron & Acute Angle of Rhombohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))
Volume of Rhombohedron = Edge Length of Rhombohedron^3*(1-cos(pi-Obtuse Angle of Rhombohedron))*sqrt(1+2*cos(pi-Obtuse Angle of Rhombohedron))
Volume of Rhombohedron = ((6*sin(Acute Angle of Rhombohedron))/(Surface to Volume Ratio of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^3*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))

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