Radius at Top and Bottom of Barrel Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius at Top and Bottom of Barrel = sqrt((3*Volume of Barrel)/(pi*Height of Barrel)-(2*Radius at Middle of Barrel^2))
rTop/Bottom = sqrt((3*V)/(pi*h)-(2*rMiddle^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 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.
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.
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 Middle of Barrel: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rTop/Bottom = sqrt((3*V)/(pi*h)-(2*rMiddle^2)) --> sqrt((3*2830)/(pi*12)-(2*10^2))
Evaluating ... ...
rTop/Bottom = 5.02038290123691
STEP 3: Convert Result to Output's Unit
5.02038290123691 Meter --> No Conversion Required
FINAL ANSWER
5.02038290123691 5.020383 Meter <-- Radius at Top and Bottom of Barrel
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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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 Top and Bottom of Barrel Formula

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

Radius at Top and Bottom of Barrel calculator uses Radius at Top and Bottom of Barrel = sqrt((3*Volume of Barrel)/(pi*Height of Barrel)-(2*Radius at Middle of Barrel^2)) to calculate the Radius at Top and Bottom of Barrel, Radius at Top and Bottom of Barrel formula is defined as the straight line connecting the center and a point on the circular base of the Barrel. Radius at Top and Bottom of Barrel is denoted by rTop/Bottom symbol.

How to calculate Radius at Top and Bottom of Barrel using this online calculator? To use this online calculator for Radius at Top and Bottom of Barrel, enter Volume of Barrel (V), Height of Barrel (h) & Radius at Middle of Barrel (rMiddle) and hit the calculate button. Here is how the Radius at Top and Bottom of Barrel calculation can be explained with given input values -> 5.020383 = sqrt((3*2830)/(pi*12)-(2*10^2)).

FAQ

What is Radius at Top and Bottom of Barrel?
Radius at Top and Bottom of Barrel formula is defined as the straight line connecting the center and a point on the circular base of the Barrel and is represented as rTop/Bottom = sqrt((3*V)/(pi*h)-(2*rMiddle^2)) or Radius at Top and Bottom of Barrel = sqrt((3*Volume of Barrel)/(pi*Height of Barrel)-(2*Radius at Middle of Barrel^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 Middle of Barrel is the radius measured at the middle of the Barrel.
How to calculate Radius at Top and Bottom of Barrel?
Radius at Top and Bottom of Barrel formula is defined as the straight line connecting the center and a point on the circular base of the Barrel is calculated using Radius at Top and Bottom of Barrel = sqrt((3*Volume of Barrel)/(pi*Height of Barrel)-(2*Radius at Middle of Barrel^2)). To calculate Radius at Top and Bottom of Barrel, you need Volume of Barrel (V), Height of Barrel (h) & Radius at Middle of Barrel (rMiddle). With our tool, you need to enter the respective value for Volume of Barrel, Height 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 Radius at Top and Bottom of Barrel?
In this formula, Radius at Top and Bottom of Barrel uses Volume of Barrel, Height of Barrel & Radius at Middle of Barrel. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Radius at Top and Bottom of Barrel = sqrt((Space Diagonal of Barrel^2-Height of Barrel^2)/4)
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