Volumes Problem (1 Viewer)

[Carrotsticks]

Here's a cool problem accessible by MX2 methods.

Consider a cylinder of unit radius and unit height, which is full of water.

a) At what angle should we tilt it such that we lose exactly 1/2 of the volume of water?

b) More generally, at what angle should we tilt it such that we lose exactly K% of water? Verify this result by subbing in K=50 into your answer to obtain the same answer as (a).

 

[asianese]

Can we assume that at 90 degrees or pi/2 all the water comes out?

 

[seanieg89]

This can be done without any integration .

 

[thorax94]

Pi/4


I mean 45 degrees.

 

[asianese]

Lol i tried that thorax...but isn't the diameter 2?

 

[Sy123]

Is answer for b:


Probably wrong

 

[asianese]

I got that too, Sy. That's when you tilt it half so that the water level is from extremity to extremity. Diamter=2 and height =1 so tantheta=1/2...