How big is the bottle?

[bonanova]

You find an old bottle, like the one shown, partially filled with liquid.
The bottom part is a circular cylinder, and the neck is tapered.
The bottle is corked, so you can't alter its contents.
Can you, using only a ruler, determine its volume?

[akaslickster]

If you look on the bottom, is there an indention where your fingers can enter? If so I definitely say impossible.

Edited June 9, 2008 by akaslickster

[Guest]

Listen carefully. Does it moake a sound? No? Zero volume.

[Guest]

Get a container, fill it with same solution.

Measure the height by using your ruler, h1

then put the bottle inside this container, let it sank at the bottom,

then measure the height by using the ruler again, h2

Measure the diameter of your container, d

the volume should be then

V = pi/4 * (d*d) * (h2-h1)

[Guest]

I assume we are looking for the volume of liquid in the bottle, not the total volume of the bottle.

So, if we can assume the neck and base indentation are conical, then measure the height (h1) and radius (r1) of the cylindrical part, the total height (h2) of the conical neck, the empty height of the neck (h3), the radius of the base of the empty part of the neck (r2) and the height of the base indetation (h4). (Remember to allow for the thickness of the glass).

Then the volume of the cylindrical part (v1) is pi x r1 x r1 x h1. The total neck volume (v2) is 1/3 x pi x r1 x r1 x h2. The empty neck volume (v3) is 1/3 x pi x r2 x r2 x h3. The indentation volume (v4) is 1/3 x pi x r1 x r1 x h4.

Therefore the complete volume of liquid is v1+v2-v3-v4, no?

[Guest]

Get a container, fill it with same solution.

Measure the height by using your ruler, h1

then put the bottle inside this container, let it sank at the bottom,

then measure the height by using the ruler again, h2

Measure the diameter of your container, d

the volume should be then

V = pi/4 * (d*d) * (h2-h1)

Hmm. This uses another container, not just a ruler.

[Guest]

It depends on whether there is enough liquid in it to fill the tapered part when it is inverted.

If there is calculate the volume of the liquid in the upright position by measuring the height of the liquid and the diameter of the base ( i am assuming no dimple in the base). You use the formula for the volume of a cylinder.

Then Invert the bottle and calculate the volume of the air space above the liquid by measuring the height above the liquid; using the same cylinder volume formula.

Then add the 2 vols together

Edited June 9, 2008 by arakis

[bonanova]

It depends on whether there is enough liquid in it to fill the tapered part when it is inverted.

If there is calculate the volume of the liquid in the upright position by measuring the height of the liquid and the diameter of the base ( i am assuming no dimple in the base). You use the formula for the volume of a cylinder.

Then Invert the bottle and calculate the volume of the air space above the liquid by measuring the height above the liquid; using the same cylinder volume formula.

Then add the 2 vols together

Hi arakis, welcome to Brainden.

You have it. Nice job.