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# Calculate pressure vessel?

A pressure vessel has a spherical end cap of radius r, it has an overall height of 6m and capacity 100m^3

Make an equation for the volume of the vessel in terms of r

Solve the equation to determine a suitable value for r.

### 2 Answers

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- King LeoLv 73 weeks agoFavourite answer
For simplicity I’ll assume the spherical end cup is a hemisphere and that 0 < r ≤ 6

Volume of cylinder + volume of hemisphere

πr²( 6 - r ) + ½ * 4/3πr³ = 100

18r² - r³ - 300/π = 0

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ignore negative values and values greater than 6

18r² - r³ - 300/π =

∴ r ≈ 2.48m

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- Anonymous3 weeks ago
I see you didn't bother picking a Best Answer.

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