Volume of Equilateral Square Pyramid given Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Equilateral Square Pyramid = (sqrt(2)/6)*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(3/2)
V = (sqrt(2)/6)*(TSA/(1+sqrt(3)))^(3/2)
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
Volume of Equilateral Square Pyramid - (Measured in Cubic Meter) - Volume of Equilateral Square Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Equilateral Square Pyramid.
Total Surface Area of Equilateral Square Pyramid - (Measured in Square Meter) - Total Surface Area of Equilateral Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Equilateral Square Pyramid.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Equilateral Square Pyramid: 270 Square Meter --> 270 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = (sqrt(2)/6)*(TSA/(1+sqrt(3)))^(3/2) --> (sqrt(2)/6)*(270/(1+sqrt(3)))^(3/2)
Evaluating ... ...
V = 231.566769112983
STEP 3: Convert Result to Output's Unit
231.566769112983 Cubic Meter --> No Conversion Required
FINAL ANSWER
231.566769112983 231.5668 Cubic Meter <-- Volume of Equilateral Square Pyramid
(Calculation completed in 00.004 seconds)

Credits

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Created by Surjojoti Som
Rashtreeya Vidyalaya College of Engineering (RVCE), Bangalore
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Verified by Harsh Raj
Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal
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10+ Equilateral Square Pyramid Calculators

Volume of Equilateral Square Pyramid given Surface Area
​ Go Volume of Equilateral Square Pyramid = (sqrt(2)/6)*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(3/2)
Height of Equilateral Pyramid given TSA
​ Go Height of Equilateral Square Pyramid = (1/sqrt(2))*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(1/2)
Edge Length of Equilateral Square Pyramid given Surface Area
​ Go Edge Length of Equilateral Square Pyramid = (Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(1/2)
Total Surface Area of Equilateral Square Pyramid
​ Go Total Surface Area of Equilateral Square Pyramid = (1+sqrt(3))*Edge Length of Equilateral Square Pyramid^2
Edge Length of Equilateral Square Pyramid given Volume
​ Go Edge Length of Equilateral Square Pyramid = ((6*Volume of Equilateral Square Pyramid)/sqrt(2))^(1/3)
Volume of Equilateral Square Pyramid
​ Go Volume of Equilateral Square Pyramid = sqrt(2)/6*Edge Length of Equilateral Square Pyramid^3
Edge Length of Equilateral Square Pyramid given Height
​ Go Edge Length of Equilateral Square Pyramid = Height of Equilateral Square Pyramid*sqrt(2)
Height of Equilateral Square Pyramid
​ Go Height of Equilateral Square Pyramid = Edge Length of Equilateral Square Pyramid/sqrt(2)
Height of Equilateral Square Pyramid given Volume
​ Go Height of Equilateral Square Pyramid = ((3*Volume of Equilateral Square Pyramid)/3)^(1/3)
Volume of Equilateral Square Pyramid given Height
​ Go Volume of Equilateral Square Pyramid = (2/3)*Height of Equilateral Square Pyramid^3

Volume of Equilateral Square Pyramid given Surface Area Formula

Volume of Equilateral Square Pyramid = (sqrt(2)/6)*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(3/2)
V = (sqrt(2)/6)*(TSA/(1+sqrt(3)))^(3/2)

What is an Equilateral Square Pyramid?

An Equilateral Square Pyramid is a pyramid with a square base and four equilateral triangular faces that intersect at a point in geometry (the apex). It has 5 faces, which include 4 equilateral triangular faces and a square base. Also, It has 5 vertices and 8 edges. It is a square pyramid whose lateral faces are equilateral triangles, which implies all the edges of are of equal length.

How to Calculate Volume of Equilateral Square Pyramid given Surface Area?

Volume of Equilateral Square Pyramid given Surface Area calculator uses Volume of Equilateral Square Pyramid = (sqrt(2)/6)*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(3/2) to calculate the Volume of Equilateral Square Pyramid, The Volume of Equilateral Square Pyramid given Surface Area formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Equilateral Square Pyramid using the TSA of the Square Pyramid. Volume of Equilateral Square Pyramid is denoted by V symbol.

How to calculate Volume of Equilateral Square Pyramid given Surface Area using this online calculator? To use this online calculator for Volume of Equilateral Square Pyramid given Surface Area, enter Total Surface Area of Equilateral Square Pyramid (TSA) and hit the calculate button. Here is how the Volume of Equilateral Square Pyramid given Surface Area calculation can be explained with given input values -> 231.5668 = (sqrt(2)/6)*(270/(1+sqrt(3)))^(3/2).

FAQ

What is Volume of Equilateral Square Pyramid given Surface Area?
The Volume of Equilateral Square Pyramid given Surface Area formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Equilateral Square Pyramid using the TSA of the Square Pyramid and is represented as V = (sqrt(2)/6)*(TSA/(1+sqrt(3)))^(3/2) or Volume of Equilateral Square Pyramid = (sqrt(2)/6)*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(3/2). Total Surface Area of Equilateral Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Equilateral Square Pyramid.
How to calculate Volume of Equilateral Square Pyramid given Surface Area?
The Volume of Equilateral Square Pyramid given Surface Area formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Equilateral Square Pyramid using the TSA of the Square Pyramid is calculated using Volume of Equilateral Square Pyramid = (sqrt(2)/6)*(Total Surface Area of Equilateral Square Pyramid/(1+sqrt(3)))^(3/2). To calculate Volume of Equilateral Square Pyramid given Surface Area, you need Total Surface Area of Equilateral Square Pyramid (TSA). With our tool, you need to enter the respective value for Total Surface Area of Equilateral Square Pyramid 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 Equilateral Square Pyramid?
In this formula, Volume of Equilateral Square Pyramid uses Total Surface Area of Equilateral Square Pyramid. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Volume of Equilateral Square Pyramid = sqrt(2)/6*Edge Length of Equilateral Square Pyramid^3
  • Volume of Equilateral Square Pyramid = (2/3)*Height of Equilateral Square Pyramid^3
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