- #1

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- Homework Statement
- Hello, I was just reading some hypothetical questions online when I came across something I was unsure how to approach.

If everyone in the world drank a glass of water from the world’s oceans how would the water level change?

I am more specifically interested in how the water level would change if only one glass of water was removed?

- Relevant Equations
- 4*π*r^2

I am not too sure how to approach this, initially I thought it may be more of a calculus and related rates of change problem, i.e. finding an expression how the volume and height of water change with respect fo time. I do not know whether this is the right idea or how to progress any further along this train of though.

You are not given any information and it is more of a thinking off the top of your head kind of problem. I have attempted a rather abstract and muddled approach to solving this problem but I would be very grateful for any alternative advice or avenues to explore. It is just a thought experiment for fun really to stretch myself so I welcome any guidance.

Moreover, firstly I thought that one should consider finding the surface area of the Earth, which since I know the radius of the Earth is approximatly 6400km this would be 4*π*r^2=4*π*6400^2=5.15*10^8km^2

Then I thought about finding the volume of the Earth being 4/3*π*r^3=4/3*π*6400^3~1.1*10^12 km^3

Then since I know that the Earth is approximately 71% covered by water this means that 71% of the surface area is water, which is about 362,100,000 km^2 of water.

A glass of water could roughly be said to contain 200ml.

I think one should find the total volume of water on Earth, I am not sure how to do this with the information I have so far. Then considering 1km^3 is equal to 1*10^12 litres one could convert this into volume into litres.

Should one then find what percentage 200ml would be of this volume, or subtract 200ml from this total volume of water on Earth?

Should one also consider the volume of water being evenly spread over the surface area of the Earth, finding how many million litres per km^2. From this one could convert from litres per km^2 to m^2 to approximate spreading this over a km^2 of Earth to find how much the water level would fall by.

Thank you to anyone who replies

You are not given any information and it is more of a thinking off the top of your head kind of problem. I have attempted a rather abstract and muddled approach to solving this problem but I would be very grateful for any alternative advice or avenues to explore. It is just a thought experiment for fun really to stretch myself so I welcome any guidance.

Moreover, firstly I thought that one should consider finding the surface area of the Earth, which since I know the radius of the Earth is approximatly 6400km this would be 4*π*r^2=4*π*6400^2=5.15*10^8km^2

Then I thought about finding the volume of the Earth being 4/3*π*r^3=4/3*π*6400^3~1.1*10^12 km^3

Then since I know that the Earth is approximately 71% covered by water this means that 71% of the surface area is water, which is about 362,100,000 km^2 of water.

A glass of water could roughly be said to contain 200ml.

I think one should find the total volume of water on Earth, I am not sure how to do this with the information I have so far. Then considering 1km^3 is equal to 1*10^12 litres one could convert this into volume into litres.

Should one then find what percentage 200ml would be of this volume, or subtract 200ml from this total volume of water on Earth?

Should one also consider the volume of water being evenly spread over the surface area of the Earth, finding how many million litres per km^2. From this one could convert from litres per km^2 to m^2 to approximate spreading this over a km^2 of Earth to find how much the water level would fall by.

Thank you to anyone who replies