Total Surface Area of Rhombohedron given Volume Calculator

✖Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the surface of the Rhombohedron.ⓘ Volume of Rhombohedron [V]			+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%

✖Total Surface Area of Rhombohedron is the total quantity of plane enclosed on the entire surface of the Rhombohedron.ⓘ Total Surface Area of Rhombohedron given Volume [TSA]

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Total Surface Area of Rhombohedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Rhombohedron = 6*(Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(2/3)*sin(Acute Angle of Rhombohedron)
TSA = 6*(V/((1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))))^(2/3)*sin(∠_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

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.
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.
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

Volume of Rhombohedron: 540 Cubic Meter --> 540 Cubic 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

TSA = 6*(V/((1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))))^(2/3)*sin(∠_Acute) --> 6*(540/((1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))))^(2/3)*sin(0.872664625997001)

Evaluating ... ...

TSA = 459.605137133267

STEP 3: Convert Result to Output's Unit

459.605137133267 Square Meter --> No Conversion Required

FINAL ANSWER

459.605137133267 ≈ 459.6051 Square Meter <-- Total Surface Area of Rhombohedron

(Calculation completed in 00.004 seconds)

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< Surface Area of Rhombohedron Calculators

Total Surface Area of Rhombohedron given Surface to Volume Ratio

LaTeX Go Total Surface Area of Rhombohedron = 6*((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))))^2*sin(Acute Angle of Rhombohedron)

Total Surface Area of Rhombohedron given Volume

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

Total Surface Area of Rhombohedron given Obtuse Angle

LaTeX Go Total Surface Area of Rhombohedron = 6*Edge Length of Rhombohedron^2*sin(pi-Obtuse Angle of Rhombohedron)

Total Surface Area of Rhombohedron

LaTeX Go Total Surface Area of Rhombohedron = 6*Edge Length of Rhombohedron^2*sin(Acute Angle of Rhombohedron)

Total Surface Area of Rhombohedron given Volume Formula

LaTeX Go

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 Total Surface Area of Rhombohedron given Volume?

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

How to calculate Total Surface Area of Rhombohedron given Volume using this online calculator? To use this online calculator for Total Surface Area of Rhombohedron given Volume, enter Volume of Rhombohedron (V) & Acute Angle of Rhombohedron (∠_Acute) and hit the calculate button. Here is how the Total Surface Area of Rhombohedron given Volume calculation can be explained with given input values -> 459.6051 = 6*(540/((1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))))^(2/3)*sin(0.872664625997001).

FAQ

What is Total Surface Area of Rhombohedron given Volume?

Total Surface Area of Rhombohedron given Volume formula is defined as the total quantity of plane enclosed on the entire surface of the Rhombohedron, calculated using its volume and is represented as TSA = 6*(V/((1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))))^(2/3)*sin(∠_Acute) or Total Surface Area of Rhombohedron = 6*(Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(2/3)*sin(Acute Angle of Rhombohedron). Volume of Rhombohedron is the total quantity of three dimensional space enclosed by the 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 Total Surface Area of Rhombohedron given Volume?

Total Surface Area of Rhombohedron given Volume formula is defined as the total quantity of plane enclosed on the entire surface of the Rhombohedron, calculated using its volume is calculated using Total Surface Area of Rhombohedron = 6*(Volume of Rhombohedron/((1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))))^(2/3)*sin(Acute Angle of Rhombohedron). To calculate Total Surface Area of Rhombohedron given Volume, you need Volume of Rhombohedron (V) & Acute Angle of Rhombohedron (∠_Acute). With our tool, you need to enter the respective value for Volume 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 Total Surface Area of Rhombohedron?

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

Total Surface Area of Rhombohedron = 6*Edge Length of Rhombohedron^2*sin(Acute Angle of Rhombohedron)
Total Surface Area of Rhombohedron = 6*Edge Length of Rhombohedron^2*sin(pi-Obtuse Angle of Rhombohedron)
Total Surface Area of Rhombohedron = 6*((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))))^2*sin(Acute Angle of Rhombohedron)

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