Total Surface Area of Tetrahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)
TSA = sqrt(3)*((12*V)/sqrt(2))^(2/3)
This formula uses 1 Functions, 2 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
Total Surface Area of Tetrahedron - (Measured in Square Meter) - Total Surface Area of Tetrahedron is the total quantity of plane enclosed by the entire surface of the Tetrahedron.
Volume of Tetrahedron - (Measured in Cubic Meter) - Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Tetrahedron: 120 Cubic Meter --> 120 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = sqrt(3)*((12*V)/sqrt(2))^(2/3) --> sqrt(3)*((12*120)/sqrt(2))^(2/3)
Evaluating ... ...
TSA = 175.304187487904
STEP 3: Convert Result to Output's Unit
175.304187487904 Square Meter --> No Conversion Required
FINAL ANSWER
175.304187487904 175.3042 Square Meter <-- Total Surface Area of Tetrahedron
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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8 Total Surface Area of Tetrahedron Calculators

Total Surface Area of Tetrahedron given Circumsphere Radius
Go Total Surface Area of Tetrahedron = sqrt(3)*((2*sqrt(2)*Circumsphere Radius of Tetrahedron)/sqrt(3))^2
Total Surface Area of Tetrahedron given Surface to Volume Ratio
Go Total Surface Area of Tetrahedron = sqrt(3)*((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^2
Total Surface Area of Tetrahedron given Midsphere Radius
Go Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(2)*Midsphere Radius of Tetrahedron)^2
Total Surface Area of Tetrahedron given Insphere Radius
Go Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2
Total Surface Area of Tetrahedron given Volume
Go Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)
Total Surface Area of Tetrahedron given Height
Go Total Surface Area of Tetrahedron = sqrt(3)*(sqrt(3/2)*Height of Tetrahedron)^2
Total Surface Area of Tetrahedron
Go Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2
Total Surface Area of Tetrahedron given Face Area
Go Total Surface Area of Tetrahedron = 4*Face Area of Tetrahedron

6 Surface Area of Tetrahedron Calculators

Total Surface Area of Tetrahedron given Circumsphere Radius
Go Total Surface Area of Tetrahedron = sqrt(3)*((2*sqrt(2)*Circumsphere Radius of Tetrahedron)/sqrt(3))^2
Total Surface Area of Tetrahedron given Volume
Go Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)
Total Surface Area of Tetrahedron given Height
Go Total Surface Area of Tetrahedron = sqrt(3)*(sqrt(3/2)*Height of Tetrahedron)^2
Total Surface Area of Tetrahedron
Go Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2
Face Area of Tetrahedron given Insphere Radius
Go Face Area of Tetrahedron = 6*sqrt(3)*Insphere Radius of Tetrahedron^2
Face Area of Tetrahedron
Go Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2

Total Surface Area of Tetrahedron given Volume Formula

Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)
TSA = sqrt(3)*((12*V)/sqrt(2))^(2/3)

What is a Tetrahedron?

A Tetrahedron is a symmetric and closed three dimensional shape with 4 identical equilateral triangular faces. It is a Platonic solid, which has 4 faces, 4 vertices and 6 edges. At each vertex, three equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Total Surface Area of Tetrahedron given Volume?

Total Surface Area of Tetrahedron given Volume calculator uses Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3) to calculate the Total Surface Area of Tetrahedron, Total Surface Area of Tetrahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Tetrahedron, and calculated using the volume of the Tetrahedron. Total Surface Area of Tetrahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Tetrahedron given Volume using this online calculator? To use this online calculator for Total Surface Area of Tetrahedron given Volume, enter Volume of Tetrahedron (V) and hit the calculate button. Here is how the Total Surface Area of Tetrahedron given Volume calculation can be explained with given input values -> 175.3042 = sqrt(3)*((12*120)/sqrt(2))^(2/3).

FAQ

What is Total Surface Area of Tetrahedron given Volume?
Total Surface Area of Tetrahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Tetrahedron, and calculated using the volume of the Tetrahedron and is represented as TSA = sqrt(3)*((12*V)/sqrt(2))^(2/3) or Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3). Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.
How to calculate Total Surface Area of Tetrahedron given Volume?
Total Surface Area of Tetrahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Tetrahedron, and calculated using the volume of the Tetrahedron is calculated using Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3). To calculate Total Surface Area of Tetrahedron given Volume, you need Volume of Tetrahedron (V). With our tool, you need to enter the respective value for Volume of Tetrahedron 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 Tetrahedron?
In this formula, Total Surface Area of Tetrahedron uses Volume of Tetrahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2
  • Total Surface Area of Tetrahedron = sqrt(3)*(sqrt(3/2)*Height of Tetrahedron)^2
  • Total Surface Area of Tetrahedron = sqrt(3)*((2*sqrt(2)*Circumsphere Radius of Tetrahedron)/sqrt(3))^2
  • Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(6)*Insphere Radius of Tetrahedron)^2
  • Total Surface Area of Tetrahedron = sqrt(3)*(2*sqrt(2)*Midsphere Radius of Tetrahedron)^2
  • Total Surface Area of Tetrahedron = sqrt(3)*((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^2
  • Total Surface Area of Tetrahedron = 4*Face Area of Tetrahedron
  • Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2
  • Total Surface Area of Tetrahedron = sqrt(3)*((2*sqrt(2)*Circumsphere Radius of Tetrahedron)/sqrt(3))^2
  • Total Surface Area of Tetrahedron = sqrt(3)*(sqrt(3/2)*Height of Tetrahedron)^2
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