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GENERATE WORK

GENERATE WORK

**Input Data : **

Top and Bottom Radius of Barrel d = 10 in

Middle Radius of Barrel D = 8 in

Height of Barrel = 25 in

**Objective : **

Find what is volume of this barrel?

**Formula **

Barrel Volume = πh12
(2D^{2} + d^{2})

**Solution :**

Barrel Volume = 3.1416 x 2512
x (2(8^{2}) + 10^{2})

= 78.539812
x (2(64) + 100)

= 6.545 x (128 + 100)

= 6.545 x 228

Barrel Volume = 1492.2565 in³

1 Cubic Inches = 0.004329 Galloon

Capacity in Galloon = (Volume in Cubic in) x 0.004328993

= 1492.2565 x 0.004328993

= 6.46

1 Galloon = 3.78541 Liters

Capacity in Liters = Capacity in Galloon x 3.78541

= 6.46 x 3.78541

= 24.4536

**cylinderical barrel volume calculator** - step by step calculation, formulas & solved example problem to find the total volume of the cylinderical barrel in different measurement units between litres (L), gallons , cubic inches, cubic foot etc from the given input values of middle & top or bottom radius. In geometry, Barrel is a large round container, usually made of wood or metal, with flat ends and, usually, curved sides. A small barrel is called as keg. The below formula & step by step calculation for example problem let the users to understand how the values are being used in such barrel volume calculations.

The following mathematical formulas are used in this calculator to find the total volume of a cylinderical barrel in litres & gallons

The below step by step calculation for example problem may be useful to understand how the values are being used in the mathematical formulas to find the volume of the cylinderical barrel.

**Example Problem :**

A cylinderical barrel having the middle radius D = 18 in, top & bottom radius d = 15 in & height h = 10 in. What is the volume of this barrel?

**Solution :**

The given values

middle radius D = 18 in

top & bottom radius d = 15 in

height h = 10 in

**Step by step calculation**

formula to find Barrel Volume = (πh/12) x (2D^{2} + d^{2})

substitute the values in the above formula

= [(π x 10)/12] [(2 x 18^{2}) + 15^{2}]

= 2.61 x 873

= 2285.50 cubic inches

1 cubic inches hold **0.016387 litres**

To find the barrel volume in litres multiply 2285.50 inches with 0.016387 litres

= 2285.50 x 0.016387

= **37.45 litres**

1 cubic inches hold **0.00432899 US liquid gallons**

To find the barrel volume in US liquid gallons multiply 2285.50 with 0.00432899 gallons

= 2285.50 x 0.00432899

= **9.89 US liquid gallons**

If the input values are in feet, refer the below table for the conversion factor. The respective conversion factor should be multiplied with the result calculated by the above mathematical formula to find the volume.

The volume of a barrel may required to be calculated in SI or metric or US customary unit systems, therefore this barrel volume calculator is featured with major measurement units conversion function to find the output values in different customary units such as litres (L), gallons (gal), cubic inches (in), cubic foott (ft), cubic meters (m), cubic centimeters (cm) & cubic millimeters (mm) by using this below conversion table.

1 cubic inch = 0.016387 litre 1 cubic inch = 0.00360464 imperial gallon 1 cubic inch = 0.00432899 US liquid gallon |
1 cubic foot = 28.3168 litres 1 cubic foot = 6.22884 imperial gallon 1 cubic foot = 7.48052 US liquid gallon |

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