# Thread: need help in determining the volume of liquid within a semispherical cylinder

1. ## need help in determining the volume of liquid within a semispherical cylinder

Hi everybody, My names noobie nooberson

It's been a long time since I've taken a math class or used anything beyond simple arithmetic, and I've forgotten so much I feel stupid. Anyway I have a problem for work and I need to figure out a formulaic way to do it.
because it will come up repeatadely.

If there were a cylinder with semi spherical ends lying with those ends to each side (like a large propane tank), and the volume of the container was 1L and the internal radius was of the container was 30cm. Then how could I determine based on the volume of liquid within the container if that liquid was was 4cm high.

I'm not sure where to start but I do think the volume formula for the hemispherical-cylinder would be helpful and I think that it would be-

V= (4/3) pi r^3 + pi r^2 L

Because the sahpe is essentially a sphere plus a cylinder. Right?

Do I need to determine L, and the use that in the next step how do I determine L and and then finish the problem? I think I need to isolate L but I forget how?

can anyone help

2. Originally Posted by Mr Wensleydale
Hi everybody, My names noobie nooberson

It's been a long time since I've taken a math class or used anything beyond simple arithmetic, and I've forgotten so much I feel stupid. Anyway I have a problem for work and I need to figure out a formulaic way to do it.
because it will come up repeatadely.

If there were a cylinder with semi spherical ends lying with those ends to each side (like a large propane tank), and the volume of the container was 1L and the internal radius was of the container was 30cm. Then how could I determine based on the volume of liquid within the container if that liquid was was 4cm high.

I'm not sure where to start but I do think the volume formula for the hemispherical-cylinder would be helpful and I think that it would be-

V= (4/3) pi r^3 + pi r^2 L

Because the sahpe is essentially a sphere plus a cylinder. Right?

Do I need to determine L, and the use that in the next step how do I determine L and and then finish the problem? I think I need to isolate L but I forget how?

can anyone help
note that the tank is laying on its side ...

the volume formula you have will determine the full volume of the tank, and is not applicable to this specific problem.

the liquid height will be measured from the bottom of the tank ...

finding the volume when the depth is 4 cm will require a special formula derived from integral calculus.

3. ## Volume of Fluid in Tank

Here are a couple websites with a calculation engine for this:

Online Conversion - Volume of a partially filled cylinder with a single hemispherical end

ABE VOLUME CALCULATORS, PARTIAL CYLINDER WITH ENDS

* TankCalc

This last one has a good explanation of exactly what is going on with the formulas. Another user, JohnS, has done this problem already in response to another question. The formulas he gererated are below:

Tank has radius R, length L for the cylinder section (total is L+2R), is horizontal, and partially filled to depth h.

Define the variable s = 1 - h/R, note that s =1 for empty tank, 0 at half full, and is -1 when full. Be sure you are using radian mode for the trig function below.

The partial volume v is given by

v = R²*L*(arccos(s) - s*SQRT(1 - s²)) + (pi/3)*R³*(1-s)²*(2+s)