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Volume of Barrel given Space Diagonal and both Radius Formula

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Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel. Check FAQs

V = \frac{π \cdot \sqrt{{d Space}^{2} - (4 \cdot {r Top/Bottom}^{2})}}{3} \cdot ((2 \cdot {r Middle}^{2}) + {r Top/Bottom}^{2})

V - Volume of Barrel?d_Space - Space Diagonal of Barrel?r_Top/Bottom - Radius at Top and Bottom of Barrel?r_Middle - Radius at Middle of Barrel?π - Archimedes' constant?

Volume of Barrel given Space Diagonal and both Radius Example

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Here is how the Volume of Barrel given Space Diagonal and both Radius equation looks like with Values.

Here is how the Volume of Barrel given Space Diagonal and both Radius equation looks like with Units.

Here is how the Volume of Barrel given Space Diagonal and both Radius equation looks like.

2942.886 = \frac{3.1416 \cdot \sqrt{16^{2} - (4 \cdot 5^{2})}}{3} \cdot ((2 \cdot 10^{2}) + 5^{2})

2942.886m³ = \frac{3.1416 \cdot \sqrt{{16m}^{2} - (4 \cdot {5m}^{2})}}{3} \cdot ((2 \cdot {10m}^{2}) + {5m}^{2})

2942.886 = \frac{3.1416 \cdot \sqrt{16^{2} - (4 \cdot 5^{2})}}{3} \cdot ((2 \cdot 10^{2}) + 5^{2})

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Volume of Barrel given Space Diagonal and both Radius Solution

Follow our step by step solution on how to calculate Volume of Barrel given Space Diagonal and both Radius?

FIRST Step Consider the formula

V = \frac{π \cdot \sqrt{{d Space}^{2} - (4 \cdot {r Top/Bottom}^{2})}}{3} \cdot ((2 \cdot {r Middle}^{2}) + {r Top/Bottom}^{2})

Next Step Substitute values of Variables

∴

V = \frac{π \cdot \sqrt{{16m}^{2} - (4 \cdot {5m}^{2})}}{3} \cdot ((2 \cdot {10m}^{2}) + {5m}^{2})

Next Step Substitute values of Constants

∴

V = \frac{3.1416 \cdot \sqrt{{16m}^{2} - (4 \cdot {5m}^{2})}}{3} \cdot ((2 \cdot {10m}^{2}) + {5m}^{2})

Next Step Prepare to Evaluate

∴

V = \frac{3.1416 \cdot \sqrt{16^{2} - (4 \cdot 5^{2})}}{3} \cdot ((2 \cdot 10^{2}) + 5^{2})

Next Step Evaluate

∴

V = 2942.88597501771m³

LAST Step Rounding Answer

∴

V = 2942.886m³

Volume of Barrel given Space Diagonal and both Radius Formula Elements

Variables

Constants

Functions

Volume of Barrel

Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Barrel

Space Diagonal of Barrel

Space Diagonal of Barrel is a line connecting two opposite vertices of barrel across its volume, that are not on the same face.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Barrel

Radius at Top and Bottom of Barrel

Radius at Top and Bottom of Barrel is the radius measured at the top and bottom of Barrel.

Symbol: r_Top/Bottom

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius at Top and Bottom of Barrel

Radius at Middle of Barrel

Radius at Middle of Barrel is the radius measured at the middle of the Barrel.

Symbol: r_Middle

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius at Middle of Barrel

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Volume of Barrel

Go Volume of Barrel

V = \frac{π \cdot h}{3} \cdot ((2 \cdot {r Middle}^{2}) + {r Top/Bottom}^{2})

Go Volume of Barrel given Height

V = \frac{π \cdot h}{3} \cdot ((2 \cdot {r Middle}^{2}) + \frac{{d Space}^{2} - h^{2}}{4})

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

Volume of Barrel given Space Diagonal and both Radius evaluator 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 evaluate 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 evaluate Volume of Barrel given Space Diagonal and both Radius using this online evaluator? To use this online evaluator 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.

FAQs on Volume of Barrel given Space Diagonal and both Radius

What is the formula to find Volume of Barrel given Space Diagonal and both Radius?

The formula of Volume of Barrel given Space Diagonal and both Radius is expressed as 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). Here is an example- 2942.886 = (pi*sqrt(16^2-(4*5^2)))/3*((2*10^2)+5^2).

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

With Space Diagonal of Barrel (d_Space), Radius at Top and Bottom of Barrel (r_Top/Bottom) & Radius at Middle of Barrel (r_Middle) we can find Volume of Barrel given Space Diagonal and both Radius using the formula - 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Barrel?

Here are the different ways to Calculate Volume of Barrel-

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)

Can the Volume of Barrel given Space Diagonal and both Radius be negative?

No, the Volume of Barrel given Space Diagonal and both Radius, measured in Volume cannot be negative.

Which unit is used to measure Volume of Barrel given Space Diagonal and both Radius?

Volume of Barrel given Space Diagonal and both Radius is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Barrel given Space Diagonal and both Radius can be measured.

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Volume of Barrel given Space Diagonal and both Radius Formula

​GoVolume of Barrel Formula

​GoVolume of Barrel given Height Formula

Volume of Barrel given Space Diagonal and both Radius Example

Volume of Barrel given Space Diagonal and both Radius Solution

Volume of Barrel given Space Diagonal and both Radius Formula Elements

Other Formulas to find Volume of Barrel

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

FAQs on Volume of Barrel given Space Diagonal and both Radius

Variable Name

GoVolume of Barrel Formula

GoVolume of Barrel given Height Formula