Volume of circular pond

[hyscore]

Hi.How do i work out the volume of a circular pond in gals/litres.It's size is 3.5 mitres across and 1 mitre deep.thanks

 

[Softus]

Assuming that the pond is of uniform diameter all the way to the bottom, the volume is:

pi * radius^2 * depth

= 3.14 * 1.75 *1.75 * 1 (my original post was wrong)
= 9.62 cubic metres

To convert to litres, you need to know that 1 cubic metre = 1000 litres.
So, the pond is 9.62 * 1000 litres, which is 9,616 litres.

To convert to gallons, you need to know that 1 gallon = 4.54 litres.
So, the pond is 9,616 / 4.54 gallons, which is 2118 gallons.

 

[masona]

2 * pi * radius * depth

= 2 * 3.14 * 1.75 * 1
= 11.00 cubic metres

Softus, is that right?

I thought it was pi x radius x radius x depth?

3.14 x 1.75m x 1.75m x 1m = 9.61 cubic metres?

Not scoring point, I'm wondering have I been doing my calculation wrong

 

[Softus]

2 * pi * radius * depth

= 2 * 3.14 * 1.75 * 1
= 11.00 cubic metres

Softus, is that right?

I thought it was pi x radius x radius x depth?

3.14 x 1.75m x 1.75m x 1m = 9.61 cubic metres?

Not scoring point, I'm wondering have I been doing my calculation wrong

Nope - you're right - I f***ed it up.

To avoid confusion, I'll edit the original. Not to cover up my error, you understand, but in case someone doesn't spot a later correction.

 

[masona]

hyscore, if you don't understand what we're talking about, this might be easier

 

[Softus]

hyscore, if you don't understand what we're talking about, this might be easier

Certainly easier, but gives the wrong answer - they call it an "estimate"!

 

[2scoops0406]

Assuming it has vertical sides, which most ponds don't!

 

[Softus]

Assuming that the pond is of uniform diameter all the way to the bottom, the volume is:

Assuming it has vertical sides, which most ponds don't!

 

[2scoops0406]

You did indeed.

 

[slippyr4]

Your pond is probably not a cylinder. If it's curved sides to a maxiumum depth of 1m, and if the sides are approximately parabolic in nature, then the ponds volume is exactly one half of the enclosing cylindrical volume. Thanks to archimedes for that. He knew his ponds.

In summary, of your pond is a curved dish shape, rather than straight sides, then the volume will be closer to 4.7 cubic metres.

 

[Softus]

...if the sides are approximately parabolic in nature, then the ponds volume is exactly one half of the enclosing cylindrical volume.

I really don't think so.

The calculus is fairly straightforward if you want the exact answer, but if you want a close approximation then it would be nearer to 45% than 50%.

And I think Newton deserves more of the credit than Archimedes!

 

[masona]

Just curious why do Hyscore need to know the volume of the pond?

Is it to calculate how many fishes is allow?

 

[slippyr4]

I really don't think so.

It's true. the volume of a rotated and constrained parabola is called a parabaloid. Archimedes proved that a parabaloid has exactly half the volume of it's containing cylinder. His book with this proof in is called "On Conoids and Spheroids". His proof did not involve calculus.

The calculus is fairly straightforward if you want the exact answer, but if you want a close approximation then it would be nearer to 45% than 50%.

And I think Newton deserves more of the credit than Archimedes!

The calculus is simple - try it! You'll get 50% as your result. Since Archimedes predated Newton by ~1900 years, i reckon he gets the credit. But if you're thanking Newton for calculus, what about Leibniz

 

[hyscore]

Thanks for replies guys the pond will be 3.5 mitres across not quite sure about depth yet,It will not have vertical sides.I wanted a rough idea to it's volume in case i add a filter and fish.