Problem

[soroban]

A cylindrical tank has a radius of 1 foot and a height of 10 feet and is completely empty.

Air is pumped in at the rate of [tex]8\pi[/tex] cubic feet per minute.

Air is leaking out at the rate of [tex]3\pi[/tex] cubic feet per minute.

When will the tank be half full?

Spoiler

How do you fill a tank half full of air?

 

[MarkFL]

Spoiler

Liquefy the air?

 

[Jameson]

Haha, I think it's clear the way they want you to do this problem and should have written it with a liquid substance. Wonder how many students didn't blink an eye at this question and did it like it was a liquid and how many were utterly confused.

Where'd you find this soroban?

 

[soroban]

Hello, Jameson!

I don't remember the source, but I've been collecting
"trick questions" all my life. ..I believe the very first one
was the classic "Where do they bury the survivors?"

Here is another . . .


A three-volume set of books is on a shelf in the usual way.
Each book has one inch of printed pages
and two covers which are a quarter-inch thick.

A bookworm start at page 1 of Volume 1 and eats his way
straight through to the last page of Volume 3.

How far does the bookwork travel?

Spoiler

The answer is not four inches.

Spoiler

Visualize the three volumes arranged
on a shelf "in the usual way".

Where is page 1 of Volume 1?
Where is the last page of Volume 3?

Answer: two inches.

 

[Ackbach]

A cylindrical tank has a radius of 1 foot and a height of 10 feet and is completely empty.

Air is pumped in at the rate of [tex]8\pi[/tex] cubic feet per minute.

Air is leaking out at the rate of [tex]3\pi[/tex] cubic feet per minute.

When will the tank be half full?

Spoiler

How do you fill a tank half full of air?

A tank is full of air when you have reached its rated pressure capacity, or when you have reached some "standard" pressure, like 2000 psig. So you redefine the meaning of the word "full" in this case. The problem can be solved, actually, if you change the original wording to read $8\pi$ and $3\pi$ standard cubic feet per minute. You would also need to define "empty". Does that mean $0$ psig? Or $0$ psia? One means simply ambient pressure, and the other means a vacuum. That would make some difference in the answer.

 

[Evgeny.Makarov]

Gases may occupy the whole container. Cats, on the other hand, just as any liquid, maintain a constant volume.

 

[MarkFL]

One of my cats frequently "fills" the bathroom sink.