Volume of Truncated Pyramid Calculator

✖Height of Truncated Pyramid is the perpendicular distance measured from the base to the top of the Truncated Pyramid.ⓘ Height of Truncated Pyramid [h]			+10% -10%
✖Base Area of Truncated Pyramid is the total amount of two-dimensional space enclosed on the base surface of the Truncated Pyramid.ⓘ Base Area of Truncated Pyramid [A_Base]			+10% -10%
✖Top Area of Truncated Pyramid is the total amount of two-dimensional space enclosed on the top surface of the Truncated Pyramid.ⓘ Top Area of Truncated Pyramid [A_Top]			+10% -10%

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

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Formula

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Volume of Truncated Pyramid

Formula

`"V" = 1/3*"h"*("A"_{"Base"}+sqrt("A"_{"Top"}*"A"_{"Base"})+"A"_{"Top"})`

Example

`"875m³"=1/3*"15m"*("100m²"+sqrt("25m²"*"100m²")+"25m²")`

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Volume of Truncated Pyramid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Truncated Pyramid = 1/3*Height of Truncated Pyramid*(Base Area of Truncated Pyramid+sqrt(Top Area of Truncated Pyramid*Base Area of Truncated Pyramid)+Top Area of Truncated Pyramid)
V = 1/3*h*(A_Base+sqrt(A_Top*A_Base)+A_Top)
This formula uses 1 Functions, 4 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 Truncated Pyramid - (Measured in Cubic Meter) - Volume of Truncated Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Truncated Pyramid.
Height of Truncated Pyramid - (Measured in Meter) - Height of Truncated Pyramid is the perpendicular distance measured from the base to the top of the Truncated Pyramid.
Base Area of Truncated Pyramid - (Measured in Square Meter) - Base Area of Truncated Pyramid is the total amount of two-dimensional space enclosed on the base surface of the Truncated Pyramid.
Top Area of Truncated Pyramid - (Measured in Square Meter) - Top Area of Truncated Pyramid is the total amount of two-dimensional space enclosed on the top surface of the Truncated Pyramid.

STEP 1: Convert Input(s) to Base Unit

Height of Truncated Pyramid: 15 Meter --> 15 Meter No Conversion Required
Base Area of Truncated Pyramid: 100 Square Meter --> 100 Square Meter No Conversion Required
Top Area of Truncated Pyramid: 25 Square Meter --> 25 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/3*h*(A_Base+sqrt(A_Top*A_Base)+A_Top) --> 1/3*15*(100+sqrt(25*100)+25)

Evaluating ... ...

V = 875

STEP 3: Convert Result to Output's Unit

875 Cubic Meter --> No Conversion Required

FINAL ANSWER

875 Cubic Meter <-- Volume of Truncated Pyramid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Pyramid » Truncated Pyramid » Volume of Truncated Pyramid

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 6 Truncated Pyramid Calculators

Lateral Surface Area of Truncated Pyramid

Go Lateral Surface Area of Truncated Pyramid = 2*(sqrt(Base Area of Truncated Pyramid)+sqrt(Top Area of Truncated Pyramid))*sqrt(((sqrt(Base Area of Truncated Pyramid)-sqrt(Top Area of Truncated Pyramid))/2)^2+Height of Truncated Pyramid^2)

Volume of Truncated Pyramid

Go Volume of Truncated Pyramid = 1/3*Height of Truncated Pyramid*(Base Area of Truncated Pyramid+sqrt(Top Area of Truncated Pyramid*Base Area of Truncated Pyramid)+Top Area of Truncated Pyramid)

Height of Truncated Pyramid

Go Height of Truncated Pyramid = (3*Volume of Truncated Pyramid)/(Base Area of Truncated Pyramid+sqrt(Top Area of Truncated Pyramid*Base Area of Truncated Pyramid)+Top Area of Truncated Pyramid)

Base Area of Truncated Pyramid

Go Base Area of Truncated Pyramid = Total Surface Area of Truncated Pyramid-(Lateral Surface Area of Truncated Pyramid+Top Area of Truncated Pyramid)

Top Area of Truncated Pyramid

Go Top Area of Truncated Pyramid = Total Surface Area of Truncated Pyramid-(Base Area of Truncated Pyramid+Lateral Surface Area of Truncated Pyramid)

Total Surface Area of Truncated Pyramid

Go Total Surface Area of Truncated Pyramid = Lateral Surface Area of Truncated Pyramid+Top Area of Truncated Pyramid+Base Area of Truncated Pyramid

Volume of Truncated Pyramid Formula

What is a Truncated Pyramid?

A Truncated Pyramid is obtained when a regular pyramid is sliced along its cross-section, creating a smaller regular pyramid. An N-sided polygon as the base of the pyramid, It has (N+2) faces, which include N isosceles triangular faces and 2 N-sided polygon faces as the base and the top surface of the Pyramid. Also, It has 2N vertices and 3N edges. A Pyramid is a polyhedron, a three-dimensional solid figure with a polygonal base and a top point called an apex.

How to Calculate Volume of Truncated Pyramid?

Volume of Truncated Pyramid calculator uses Volume of Truncated Pyramid = 1/3*Height of Truncated Pyramid*(Base Area of Truncated Pyramid+sqrt(Top Area of Truncated Pyramid*Base Area of Truncated Pyramid)+Top Area of Truncated Pyramid) to calculate the Volume of Truncated Pyramid, Volume of Truncated Pyramid formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Truncated Pyramid. Volume of Truncated Pyramid is denoted by V symbol.

How to calculate Volume of Truncated Pyramid using this online calculator? To use this online calculator for Volume of Truncated Pyramid, enter Height of Truncated Pyramid (h), Base Area of Truncated Pyramid (A_Base) & Top Area of Truncated Pyramid (A_Top) and hit the calculate button. Here is how the Volume of Truncated Pyramid calculation can be explained with given input values -> 875 = 1/3*15*(100+sqrt(25*100)+25).

FAQ

What is Volume of Truncated Pyramid?

Volume of Truncated Pyramid formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Truncated Pyramid and is represented as V = 1/3*h*(A_Base+sqrt(A_Top*A_Base)+A_Top) or Volume of Truncated Pyramid = 1/3*Height of Truncated Pyramid*(Base Area of Truncated Pyramid+sqrt(Top Area of Truncated Pyramid*Base Area of Truncated Pyramid)+Top Area of Truncated Pyramid). Height of Truncated Pyramid is the perpendicular distance measured from the base to the top of the Truncated Pyramid, Base Area of Truncated Pyramid is the total amount of two-dimensional space enclosed on the base surface of the Truncated Pyramid & Top Area of Truncated Pyramid is the total amount of two-dimensional space enclosed on the top surface of the Truncated Pyramid.

How to calculate Volume of Truncated Pyramid?

Volume of Truncated Pyramid formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Truncated Pyramid is calculated using Volume of Truncated Pyramid = 1/3*Height of Truncated Pyramid*(Base Area of Truncated Pyramid+sqrt(Top Area of Truncated Pyramid*Base Area of Truncated Pyramid)+Top Area of Truncated Pyramid). To calculate Volume of Truncated Pyramid, you need Height of Truncated Pyramid (h), Base Area of Truncated Pyramid (A_Base) & Top Area of Truncated Pyramid (A_Top). With our tool, you need to enter the respective value for Height of Truncated Pyramid, Base Area of Truncated Pyramid & Top Area of Truncated Pyramid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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