Radius at Middle of Barrel Calculator

✖Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel.ⓘ Volume of Barrel [V]			+10% -10%
✖Height of Barrel is the measure of Barrel from base to top.ⓘ Height of Barrel [h]			+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]

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Formula

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Radius at Middle of Barrel

Formula

`"r"_{"Middle"} = sqrt(((3*"V")/(pi*"h")-"r"_{"Top/Bottom"}^2)/2)`

Example

`"10.0051m"=sqrt(((3*"2830m³")/(pi*"12m")-("5m")^2)/2)`

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Radius at Middle of Barrel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius at Middle of Barrel = sqrt(((3*Volume of Barrel)/(pi*Height of Barrel)-Radius at Top and Bottom of Barrel^2)/2)
r_Middle = sqrt(((3*V)/(pi*h)-r_Top/Bottom^2)/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

Radius at Middle of Barrel - (Measured in Meter) - Radius at Middle of Barrel is the radius measured at the middle of the Barrel.
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 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.

STEP 1: Convert Input(s) to Base Unit

Volume of Barrel: 2830 Cubic Meter --> 2830 Cubic Meter No Conversion Required
Height of Barrel: 12 Meter --> 12 Meter No Conversion Required
Radius at Top and Bottom of Barrel: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_Middle = sqrt(((3*V)/(pi*h)-r_Top/Bottom^2)/2) --> sqrt(((3*2830)/(pi*12)-5^2)/2)

Evaluating ... ...

r_Middle = 10.0051048089221

STEP 3: Convert Result to Output's Unit

10.0051048089221 Meter --> No Conversion Required

FINAL ANSWER

10.0051048089221 ≈ 10.0051 Meter <-- Radius at Middle of Barrel

(Calculation completed in 00.020 seconds)

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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

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< 3 Radius of Barrel Calculators

Radius at Top and Bottom of Barrel

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

Radius at Middle of Barrel

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

Radius at Top and Bottom of Barrel given Space Diagonal and Height

Go Radius at Top and Bottom of Barrel = sqrt((Space Diagonal of Barrel^2-Height of Barrel^2)/4)

Radius at Middle of Barrel Formula

Radius at Middle of Barrel = sqrt(((3*Volume of Barrel)/(pi*Height of Barrel)-Radius at Top and Bottom of Barrel^2)/2)
r_Middle = sqrt(((3*V)/(pi*h)-r_Top/Bottom^2)/2)

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 Radius at Middle of Barrel?

Radius at Middle of Barrel calculator uses Radius at Middle of Barrel = sqrt(((3*Volume of Barrel)/(pi*Height of Barrel)-Radius at Top and Bottom of Barrel^2)/2) to calculate the Radius at Middle of Barrel, Radius at Middle of Barrel formula is defined as the straight line connecting a point on the center of the line passing which divides the Barrel into two equal parts equally and a point on its curvature part. Radius at Middle of Barrel is denoted by r_Middle symbol.

How to calculate Radius at Middle of Barrel using this online calculator? To use this online calculator for Radius at Middle of Barrel, enter Volume of Barrel (V), Height of Barrel (h) & Radius at Top and Bottom of Barrel (r_Top/Bottom) and hit the calculate button. Here is how the Radius at Middle of Barrel calculation can be explained with given input values -> 10.0051 = sqrt(((3*2830)/(pi*12)-5^2)/2).

FAQ

What is Radius at Middle of Barrel?

Radius at Middle of Barrel formula is defined as the straight line connecting a point on the center of the line passing which divides the Barrel into two equal parts equally and a point on its curvature part and is represented as r_Middle = sqrt(((3*V)/(pi*h)-r_Top/Bottom^2)/2) or Radius at Middle of Barrel = sqrt(((3*Volume of Barrel)/(pi*Height of Barrel)-Radius at Top and Bottom of Barrel^2)/2). Volume of Barrel is the amount of three dimensional space covered by the closed surface of Barrel, Height of Barrel is the measure of Barrel from base to top & Radius at Top and Bottom of Barrel is the radius measured at the top and bottom of Barrel.

How to calculate Radius at Middle of Barrel?

Radius at Middle of Barrel formula is defined as the straight line connecting a point on the center of the line passing which divides the Barrel into two equal parts equally and a point on its curvature part is calculated using Radius at Middle of Barrel = sqrt(((3*Volume of Barrel)/(pi*Height of Barrel)-Radius at Top and Bottom of Barrel^2)/2). To calculate Radius at Middle of Barrel, you need Volume of Barrel (V), Height of Barrel (h) & Radius at Top and Bottom of Barrel (r_Top/Bottom). With our tool, you need to enter the respective value for Volume of Barrel, Height of Barrel & Radius at Top and Bottom of Barrel 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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