Volume of Barrel given Height Calculator

✖Height of Barrel is the measure of Barrel from base to top.ⓘ Height of Barrel [h]			+10% -10%
✖Radius at Middle of Barrel is the radius measured at the middle of the Barrel.ⓘ Radius at Middle of Barrel [r_Middle]			+10% -10%
✖Space Diagonal of Barrel is a line connecting two opposite vertices of barrel across its volume, that are not on the same face.ⓘ Space Diagonal of Barrel [d_Space]			+10% -10%

✖Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel.ⓘ Volume of Barrel given Height [V]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Barrel Formulas PDF PDF Image

Volume of Barrel given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+(Space Diagonal of Barrel^2-Height of Barrel^2)/4)
V = (pi*h)/3*((2*r_Middle^2)+(d_Space^2-h^2)/4)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Barrel - (Measured in Cubic Meter) - Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel.
Height of Barrel - (Measured in Meter) - Height of Barrel is the measure of Barrel from base to top.
Radius at Middle of Barrel - (Measured in Meter) - Radius at Middle of Barrel is the radius measured at the middle of the Barrel.
Space Diagonal of Barrel - (Measured in Meter) - Space Diagonal of Barrel is a line connecting two opposite vertices of barrel across its volume, that are not on the same face.

STEP 1: Convert Input(s) to Base Unit

Height of Barrel: 12 Meter --> 12 Meter No Conversion Required
Radius at Middle of Barrel: 10 Meter --> 10 Meter No Conversion Required
Space Diagonal of Barrel: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (pi*h)/3*((2*r_Middle^2)+(d_Space^2-h^2)/4) --> (pi*12)/3*((2*10^2)+(16^2-12^2)/4)

Evaluating ... ...

V = 2865.13250007389

STEP 3: Convert Result to Output's Unit

2865.13250007389 Cubic Meter --> No Conversion Required

FINAL ANSWER

2865.13250007389 ≈ 2865.133 Cubic Meter <-- Volume of Barrel

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Barrel » Volume of Barrel » Volume of Barrel given Height

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1800+ more calculators!

< Volume of Barrel Calculators

Volume of Barrel given Space Diagonal and both Radius

LaTeX Go Volume of Barrel = (pi*sqrt(Space Diagonal of Barrel^2-(4*Radius at Top and Bottom of Barrel^2)))/3*((2*Radius at Middle of Barrel^2)+Radius at Top and Bottom of Barrel^2)

Volume of Barrel given Height

LaTeX Go Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+(Space Diagonal of Barrel^2-Height of Barrel^2)/4)

Volume of Barrel

LaTeX Go Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+Radius at Top and Bottom of Barrel^2)

Volume of Barrel given Height Formula

LaTeX Go

Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+(Space Diagonal of Barrel^2-Height of Barrel^2)/4)
V = (pi*h)/3*((2*r_Middle^2)+(d_Space^2-h^2)/4)

What is Barrel?

A Barrel or cask is a hollow cylindrical container with a bulging center, longer than it is wide. They are traditionally made of wooden staves and bound by wooden or metal hoops. The word vat is often used for large containers for liquids, usually alcoholic beverages; a small barrel or cask is known as a keg.The barrel has also been used as a standard size of measure referring to a set capacity or weight of a given commodity.

How to Calculate Volume of Barrel given Height?

Volume of Barrel given Height calculator uses Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+(Space Diagonal of Barrel^2-Height of Barrel^2)/4) to calculate the Volume of Barrel, Volume of Barrel given Height formula is defined as the amount of three-dimensional space occupied by the closed surface of the Barrel, calculated using height, space diagonal, and radius at the middle of the Barrel. Volume of Barrel is denoted by V symbol.

How to calculate Volume of Barrel given Height using this online calculator? To use this online calculator for Volume of Barrel given Height, enter Height of Barrel (h), Radius at Middle of Barrel (r_Middle) & Space Diagonal of Barrel (d_Space) and hit the calculate button. Here is how the Volume of Barrel given Height calculation can be explained with given input values -> 2865.133 = (pi*12)/3*((2*10^2)+(16^2-12^2)/4).

FAQ

What is Volume of Barrel given Height?

Volume of Barrel given Height formula is defined as the amount of three-dimensional space occupied by the closed surface of the Barrel, calculated using height, space diagonal, and radius at the middle of the Barrel and is represented as V = (pi*h)/3*((2*r_Middle^2)+(d_Space^2-h^2)/4) or Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+(Space Diagonal of Barrel^2-Height of Barrel^2)/4). Height of Barrel is the measure of Barrel from base to top, Radius at Middle of Barrel is the radius measured at the middle of the Barrel & Space Diagonal of Barrel is a line connecting two opposite vertices of barrel across its volume, that are not on the same face.

How to calculate Volume of Barrel given Height?

Volume of Barrel given Height formula is defined as the amount of three-dimensional space occupied by the closed surface of the Barrel, calculated using height, space diagonal, and radius at the middle of the Barrel is calculated using Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+(Space Diagonal of Barrel^2-Height of Barrel^2)/4). To calculate Volume of Barrel given Height, you need Height of Barrel (h), Radius at Middle of Barrel (r_Middle) & Space Diagonal of Barrel (d_Space). With our tool, you need to enter the respective value for Height of Barrel, Radius at Middle of Barrel & Space Diagonal of Barrel 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 Barrel?

In this formula, Volume of Barrel uses Height of Barrel, Radius at Middle of Barrel & Space Diagonal of Barrel. We can use 2 other way(s) to calculate the same, which is/are as follows -

Volume of Barrel = (pi*Height of Barrel)/3*((2*Radius at Middle of Barrel^2)+Radius at Top and Bottom of Barrel^2)
Volume of Barrel = (pi*sqrt(Space Diagonal of Barrel^2-(4*Radius at Top and Bottom of Barrel^2)))/3*((2*Radius at Middle of Barrel^2)+Radius at Top and Bottom of Barrel^2)

Home

FREE PDFs

🔍 Search