Volume of Square Pyramid given Slant Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4)
V = 1/3*le(Base)^2*sqrt(hslant^2-(le(Base)^2)/4)
This formula uses 1 Functions, 3 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 Square Pyramid - (Measured in Cubic Meter) - Volume of Square Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid.
Edge Length of Base of Square Pyramid - (Measured in Meter) - Edge Length of Base of Square Pyramid is the length of the straight line connecting any two adjacent vertices of the base of the Square Pyramid.
Slant Height of Square Pyramid - (Measured in Meter) - Slant Height of Square Pyramid is the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Base of Square Pyramid: 10 Meter --> 10 Meter No Conversion Required
Slant Height of Square Pyramid: 16 Meter --> 16 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = 1/3*le(Base)^2*sqrt(hslant^2-(le(Base)^2)/4) --> 1/3*10^2*sqrt(16^2-(10^2)/4)
Evaluating ... ...
V = 506.622805119022
STEP 3: Convert Result to Output's Unit
506.622805119022 Cubic Meter --> No Conversion Required
FINAL ANSWER
506.622805119022 506.6228 Cubic Meter <-- Volume of Square Pyramid
(Calculation completed in 00.004 seconds)

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Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Indian Institute of Information Technology (IIIT), Bhopal
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Volume of Square Pyramid Calculators

Volume of Square Pyramid given Lateral Edge Length
​ LaTeX ​ Go Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Lateral Edge Length of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/2)
Volume of Square Pyramid given Slant Height
​ LaTeX ​ Go Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4)
Volume of Square Pyramid given Slant Height and Height
​ LaTeX ​ Go Volume of Square Pyramid = 1/3*Height of Square Pyramid*(4*(Slant Height of Square Pyramid^2-Height of Square Pyramid^2))
Volume of Square Pyramid
​ LaTeX ​ Go Volume of Square Pyramid = (Edge Length of Base of Square Pyramid^2*Height of Square Pyramid)/3

Important Formulas of Regular Square Pyramid Calculators

Base Angle of Square Pyramid
​ LaTeX ​ Go Base Angle of Square Pyramid = arccos(((Edge Length of Base of Square Pyramid/2)^2+Slant Height of Square Pyramid^2-Height of Square Pyramid^2)/(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid))
Lateral Edge Length of Square Pyramid
​ LaTeX ​ Go Lateral Edge Length of Square Pyramid = sqrt(Edge Length of Base of Square Pyramid^2/2+Height of Square Pyramid^2)
Slant Height of Square Pyramid
​ LaTeX ​ Go Slant Height of Square Pyramid = sqrt((Edge Length of Base of Square Pyramid^2)/4+Height of Square Pyramid^2)
Base Area of Square Pyramid
​ LaTeX ​ Go Base Area of Square Pyramid = Edge Length of Base of Square Pyramid^2

Volume of Square Pyramid given Slant Height Formula

​LaTeX ​Go
Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4)
V = 1/3*le(Base)^2*sqrt(hslant^2-(le(Base)^2)/4)

What is a Square Pyramid?

A Square Pyramid is a pyramid with a square base and four isosceles triangular faces that intersect at a point in geometry (the apex). It has 5 faces, which include 4 isosceles triangular faces and a square base. Also, It has 5 vertices and 8 edges.

How to Calculate Volume of Square Pyramid given Slant Height?

Volume of Square Pyramid given Slant Height calculator uses Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4) to calculate the Volume of Square Pyramid, Volume of Square Pyramid given Slant Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid and is calculated using the slant height of the Square Pyramid. Volume of Square Pyramid is denoted by V symbol.

How to calculate Volume of Square Pyramid given Slant Height using this online calculator? To use this online calculator for Volume of Square Pyramid given Slant Height, enter Edge Length of Base of Square Pyramid (le(Base)) & Slant Height of Square Pyramid (hslant) and hit the calculate button. Here is how the Volume of Square Pyramid given Slant Height calculation can be explained with given input values -> 506.6228 = 1/3*10^2*sqrt(16^2-(10^2)/4).

FAQ

What is Volume of Square Pyramid given Slant Height?
Volume of Square Pyramid given Slant Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid and is calculated using the slant height of the Square Pyramid and is represented as V = 1/3*le(Base)^2*sqrt(hslant^2-(le(Base)^2)/4) or Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4). Edge Length of Base of Square Pyramid is the length of the straight line connecting any two adjacent vertices of the base of the Square Pyramid & Slant Height of Square Pyramid is the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face.
How to calculate Volume of Square Pyramid given Slant Height?
Volume of Square Pyramid given Slant Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid and is calculated using the slant height of the Square Pyramid is calculated using Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4). To calculate Volume of Square Pyramid given Slant Height, you need Edge Length of Base of Square Pyramid (le(Base)) & Slant Height of Square Pyramid (hslant). With our tool, you need to enter the respective value for Edge Length of Base of Square Pyramid & Slant Height of 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 Square Pyramid?
In this formula, Volume of Square Pyramid uses Edge Length of Base of Square Pyramid & Slant Height of Square Pyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Volume of Square Pyramid = (Edge Length of Base of Square Pyramid^2*Height of Square Pyramid)/3
  • Volume of Square Pyramid = 1/3*Height of Square Pyramid*(4*(Slant Height of Square Pyramid^2-Height of Square Pyramid^2))
  • Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Lateral Edge Length of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/2)
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