Surface to Volume Ratio of Rhombohedron Calculator

✖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%
✖Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron.ⓘ Edge Length of Rhombohedron [l_e]			+10% -10%

✖Surface to Volume Ratio of Rhombohedron is the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron.ⓘ Surface to Volume Ratio of Rhombohedron [R_A/V]

⎘ Copy

👎

Formula

✖

Surface to Volume Ratio of Rhombohedron

Formula

`"R"_{"A/V"} = (6*sin("∠"_{"Acute"}))/("l"_{"e"}*(1-cos("∠"_{"Acute"}))*sqrt(1+2*cos("∠"_{"Acute"})))`

Example

`"0.851101m⁻¹"=(6*sin("50°"))/("10m"*(1-cos("50°"))*sqrt(1+2*cos("50°")))`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

Surface to Volume Ratio of Rhombohedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron)))
R_A/V = (6*sin(∠_Acute))/(l_e*(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

Surface to Volume Ratio of Rhombohedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Rhombohedron is the numerical ratio of the total surface area of a Rhombohedron to the volume 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.
Edge Length of Rhombohedron - (Measured in Meter) - Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron.

STEP 1: Convert Input(s) to Base Unit

Acute Angle of Rhombohedron: 50 Degree --> 0.872664625997001 Radian (Check conversion here)
Edge Length of Rhombohedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (6*sin(∠_Acute))/(l_e*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))) --> (6*sin(0.872664625997001))/(10*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001)))

Evaluating ... ...

R_A/V = 0.851100691004427

STEP 3: Convert Result to Output's Unit

0.851100691004427 1 per Meter --> No Conversion Required

FINAL ANSWER

0.851100691004427 ≈ 0.851101 1 per Meter <-- Surface to Volume Ratio of Rhombohedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Rhombohedron » Surface to Volume Ratio of Rhombohedron » Surface to Volume Ratio of Rhombohedron

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< 4 Surface to Volume Ratio of Rhombohedron Calculators

Surface to Volume Ratio of Rhombohedron given Volume

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

Surface to Volume Ratio of Rhombohedron given Total Surface Area

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

Surface to Volume Ratio of Rhombohedron given Obtuse Angle

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

Surface to Volume Ratio of Rhombohedron

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

Surface to Volume Ratio of Rhombohedron 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 Surface to Volume Ratio of Rhombohedron?

Surface to Volume Ratio of Rhombohedron calculator uses Surface to Volume Ratio of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))) to calculate the Surface to Volume Ratio of Rhombohedron, Surface to Volume Ratio of Rhombohedron formula is defined as the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron. Surface to Volume Ratio of Rhombohedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Rhombohedron using this online calculator? To use this online calculator for Surface to Volume Ratio of Rhombohedron, enter Acute Angle of Rhombohedron (∠_Acute) & Edge Length of Rhombohedron (l_e) and hit the calculate button. Here is how the Surface to Volume Ratio of Rhombohedron calculation can be explained with given input values -> 0.851101 = (6*sin(0.872664625997001))/(10*(1-cos(0.872664625997001))*sqrt(1+2*cos(0.872664625997001))).

FAQ

What is Surface to Volume Ratio of Rhombohedron?

Surface to Volume Ratio of Rhombohedron formula is defined as the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron and is represented as R_A/V = (6*sin(∠_Acute))/(l_e*(1-cos(∠_Acute))*sqrt(1+2*cos(∠_Acute))) or Surface to Volume Ratio of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))). Acute Angle of Rhombohedron is the angle of any of the six rhombus faces of the Rhombohedron, which is less than 90 degrees & Edge Length of Rhombohedron is the distance between any pair of adjacent vertices of the Rhombohedron.

How to calculate Surface to Volume Ratio of Rhombohedron?

Surface to Volume Ratio of Rhombohedron formula is defined as the numerical ratio of the total surface area of a Rhombohedron to the volume of the Rhombohedron is calculated using Surface to Volume Ratio of Rhombohedron = (6*sin(Acute Angle of Rhombohedron))/(Edge Length of Rhombohedron*(1-cos(Acute Angle of Rhombohedron))*sqrt(1+2*cos(Acute Angle of Rhombohedron))). To calculate Surface to Volume Ratio of Rhombohedron, you need Acute Angle of Rhombohedron (∠_Acute) & Edge Length of Rhombohedron (l_e). With our tool, you need to enter the respective value for Acute Angle of Rhombohedron & Edge Length 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 Surface to Volume Ratio of Rhombohedron?

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

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

Home

FREE PDFs

🔍 Search