Volume of Barrel given Space Diagonal and both Radius Calculator

✖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%
✖Radius at Top and Bottom of Barrel is the radius measured at the top and bottom of Barrel.ⓘ Radius at Top and Bottom of Barrel [r_Top/Bottom]			+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%

✖Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel.ⓘ Volume of Barrel given Space Diagonal and both Radius [V]

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Volume of Barrel given Space Diagonal and both Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V = (pi*sqrt(d_Space^2-(4*r_Top/Bottom^2)))/3*((2*r_Middle^2)+r_Top/Bottom^2)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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 Barrel - (Measured in Cubic Meter) - Volume of Barrel is the amount of three dimensional space covered by the closed surface of 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.
Radius at Top and Bottom of Barrel - (Measured in Meter) - Radius at Top and Bottom of Barrel is the radius measured at the top and bottom of Barrel.
Radius at Middle of Barrel - (Measured in Meter) - Radius at Middle of Barrel is the radius measured at the middle of the Barrel.

STEP 1: Convert Input(s) to Base Unit

Space Diagonal of Barrel: 16 Meter --> 16 Meter No Conversion Required
Radius at Top and Bottom of Barrel: 5 Meter --> 5 Meter No Conversion Required
Radius at Middle of Barrel: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (pi*sqrt(d_Space^2-(4*r_Top/Bottom^2)))/3*((2*r_Middle^2)+r_Top/Bottom^2) --> (pi*sqrt(16^2-(4*5^2)))/3*((2*10^2)+5^2)

Evaluating ... ...

V = 2942.88597501771

STEP 3: Convert Result to Output's Unit

2942.88597501771 Cubic Meter --> No Conversion Required

FINAL ANSWER

2942.88597501771 ≈ 2942.886 Cubic Meter <-- Volume of Barrel

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< 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 Space Diagonal and both Radius Formula

LaTeX Go

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 Space Diagonal and both Radius?

Volume of Barrel given Space Diagonal and both Radius calculator uses 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) to calculate the Volume of Barrel, Volume of Barrel given Space Diagonal and both Radius formula is defined as the amount of three-dimensional space occupied by the closed surface of the Barrel, calculated using space diagonal and both the radius of the Barrel. Volume of Barrel is denoted by V symbol.

How to calculate Volume of Barrel given Space Diagonal and both Radius using this online calculator? To use this online calculator for Volume of Barrel given Space Diagonal and both Radius, enter Space Diagonal of Barrel (d_Space), Radius at Top and Bottom of Barrel (r_Top/Bottom) & Radius at Middle of Barrel (r_Middle) and hit the calculate button. Here is how the Volume of Barrel given Space Diagonal and both Radius calculation can be explained with given input values -> 2942.886 = (pi*sqrt(16^2-(4*5^2)))/3*((2*10^2)+5^2).

FAQ

What is Volume of Barrel given Space Diagonal and both Radius?

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

How to calculate Volume of Barrel given Space Diagonal and both Radius?

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

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