how do i measure the exact volume of water in a bucket?

anonymous 28

New member
Joined
May 12, 2013
Messages
5
How do i measure the exact volume of water in a bucket (a tapered cone shaped) especially when i do not know d exact height assuming if it is a perfect cone? Please advise.
 
How do i measure the exact volume of water in a bucket (a tapered cone shaped) especially when i do not know d exact height assuming if it is a perfect cone? Please advise.
If it is a right cone (which is what I suspect you mean by a perfect cone), you can use the Pythagorean Theorem to find the height. Measure the diameter of the base. Divide that number by 2 to calculate the radius r. Now measure the slant height s from the tip of the cone along its side to the base. The vertical height of the cone is:

\(\displaystyle h = \sqrt{s^2 - r^2}.\)
 
If it is a right cone (which is what I suspect you mean by a perfect cone), you can use the Pythagorean Theorem to find the height. Measure the diameter of the base. Divide that number by 2 to calculate the radius r. Now measure the slant height s from the tip of the cone along its side to the base. The vertical height of the cone is:

\(\displaystyle h = \sqrt{s^2 - r^2}.\)

What if the length of the slant from d tip of cone to its side base is not known.
 
What if the length of the slant from d tip of cone to its side base is not known.
Is this a real cone? In that case, you measure things. Take a string. Hold one end at any point along the circumference of the base and pull it taut to the tip. Now measure that length of string against a ruler. That is the slant height. If you have calipers, you can measure it more exactly.

If you are dealing with an imaginary cone, you need information. What pieces of information do you have?
 
Also - in general - buckets are truncated cone (as opposed to a cone like ice-cream cone).
 
and nobody can ever MEASURE exact volume of anything .... calculate yes (maybe) .... measure no (Mr. Heisenberg's ghost will get you...)
 
Is this a real cone? In that case, you measure things. Take a string. Hold one end at any point along the circumference of the base and pull it taut to the tip. Now measure that length of string against a ruler. That is the slant height. If you have calipers, you can measure it more exactly.

If you are dealing with an imaginary cone, you need information. What pieces of information do you have?

I have only the measurement of the diameter and the height of the bucket.
 
I have only the measurement of the diameter and the height of the bucket.

Since there is no other restriction - assume it is a cylindrical bucket.

So then

Given height and diameter - what is the internal volume of a hollow cylinder?
 
How do i measure the exact volume of water in a bucket (a tapered cone shaped) especially when i do not know d exact height assuming if it is a perfect cone? Please advise.
I have only the measurement of the diameter and the height of the bucket.
If you DO have the diameter and also the height,
and if it IS a perfect cone,
then the volume is

........\(\displaystyle \displaystyle V_{cone} = \dfrac{1}{3} \pi r^2\ h \)
 
Now you've got the height? You originally said you didn't: are you fooling around?

Anyway, if your bucket is a cut-off cone, then that's not enough information.

It's a somewhat a cut off cone shape...i can only measure the diameter of the bucket base, diameter top bucket and the bucket height.
 
Volume = h(T + 4M+ B)/6

T= area of Top circular opening
M= area of cross-section half way up (avg of 2 diameters)
B= area of bottom circle
h= height
 
WHY didn't you say this in your FIRST post?:confused:

Let base RADIUS = a and top RADIUS = b and height = h
V = pi*h(a^2 + 2ab + b^2) / 3

Next time you post a problem, please be COMPLETE.


Sorry Denis. The bucket is somewhat look like the picture below.
913.jpg


Thanks for the formula. I'm gonna try use it on my water evaporation test. :)
 
A typo in the formula ?

WHY didn't you say this in your FIRST post?:confused:

Let base RADIUS = a and top RADIUS = b and height = h
V = pi*h(a^2 + 2ab + b^2) / 3

Next time you post a problem, please be COMPLETE.

I believe it should just be "ab" and not "2ab" in the above formula, so the formula should read:

V = pi*h(a^2 + ab + b^2) / 3 ?
 
Top