How Do You Calculate the Volume of Liquid in a Partially Filled Conical Glass?

AI Thread Summary
To calculate the volume of liquid in a partially filled conical glass, one must define the height of the glass (H) and the height of the liquid (h). The volume of a cone is given by the formula V = (1/3)πr²H, where r is the radius at height h. The challenge lies in finding the relationship between the radius and height using similar triangles, which affects the volume calculation. The initial approach led to the incorrect ratio of H:2h, highlighting the need to consider how the radius changes as the height of the liquid changes. Understanding these relationships is crucial for accurately determining the volume of liquid in the cone.
skiing4free
Messages
20
Reaction score
0
This is a problem that my lecturer gave us in class and it has been bugging me ever since. I have been unsuccesful in finding or calculating a proper solution so I am hoping PF will be able to help...

This is the Q:

Let H be the height of a conical glass which is filled to a height h. Find the volume of the liquid in the glass as a proportion of the volume if the glass is full. Find the ratio h/H for which the glass is half full.
To answer this question you must construct a mathematical model defining all the variables.

This does not sound like a difficult question to solve but whenever I try to solve with simple conical volume equations I just get that the ratio is H:2h which is obviously not right. Any help would be greatly appreciated.
 
Mathematics news on Phys.org
Why don't you explain how you got H:2h?
 
Well the formula for a volume of a cone is:
V=1/3*pi*r^2*H.

V1 which is the volume of the full cone and V2 is the volume of the half full cone it is clear that V1/2=V2. I put the volume equations into this with the two differnt heights and when the constants are removed (pi, 1/3) you are left with H=2h. ahh but i have just seen how the radius would of course change... Now I think I am more confused
 
Can you find a relationship between what the radius and the height is going to be when you're at a certain height up the cone? (hint: think similar triangles)
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

I How do I calculate density given height and volume?
Replies
7
Views
2K
What to fill a glass bottle with (a liquid that hardens) to lower its volume?
Replies
24
Views
3K
The volume of a "spherical cap" using triple integrals
Replies
9
Views
1K
How does water rise along a glass plate? (surface tension question)
Replies
2
Views
1K
How Is Destructive Interference Achieved in a Liquid Film on Glass?
Replies
2
Views
2K
I How to find the change in volume of a solid to a liquid
Replies
3
Views
1K
MHB How do I get the book's answer for finding the area of a gable?
Replies
4
Views
1K
Spirit evaporating from a bowl
Replies
33
Views
3K
Pressure in a Fluid-Filled Glass with a Side-Hole Tube: Is Pa = Pb = Pc?
Replies
1
Views
2K
A block dropping onto a spring system
2
Replies
58
Views
2K

Hot Threads

Recent Insights

Back
Top