Volume of Square Pyramid given Slant Height Calculator

✖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.ⓘ Edge Length of Base of Square Pyramid [l_e(Base)]			+10% -10%
✖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.ⓘ Slant Height of Square Pyramid [h_slant]			+10% -10%

✖Volume of Square Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid.ⓘ Volume of Square Pyramid given Slant Height [V]

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Formula

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Volume of Square Pyramid given Slant Height

Formula

`"V" = 1/3*"l"_{"e(Base)"}^2*sqrt("h"_{"slant"}^2-("l"_{"e(Base)"}^2)/4)`

Example

`"506.6228m³"=1/3*("10m")^2*sqrt(("16m")^2-(("10m")^2)/4)`

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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*l_e(Base)^2*sqrt(h_slant^2-(l_e(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*l_e(Base)^2*sqrt(h_slant^2-(l_e(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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Home » Math » Geometry » 3D Geometry » Pyramid » Square Pyramid » Square Pyramid » Volume of Square Pyramid » Volume of Square Pyramid given Slant Height

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 5 Volume of Square Pyramid Calculators

Volume of Square Pyramid given Lateral Edge Length

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

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 Lateral Edge Length and Height

Go Volume of Square Pyramid = 1/3*Height of Square Pyramid*(2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))

Volume of Square Pyramid given Slant Height and Height

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

Go Volume of Square Pyramid = (Edge Length of Base of Square Pyramid^2* Height of Square Pyramid)/3

Volume of Square Pyramid given Slant Height Formula

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 (l_e(Base)) & Slant Height of Square Pyramid (h_slant) 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*l_e(Base)^2*sqrt(h_slant^2-(l_e(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 (l_e(Base)) & Slant Height of Square Pyramid (h_slant). 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 4 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)
Volume of Square Pyramid = 1/3*Height of Square Pyramid*(2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))

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