Integration to Solve, points on a cylinder

[katmarie]

Homework Statement

"A cylindrical tank is buried beneath a lake in order to safely store radioactive waste. Inside the tank is a measuring rod that identifies the level of radioactive waste.
Determine the points on the measuring rod that would identify when the tank is 1/4 , 1/2 and 3/4 full.
Assume the diameter of the cylinder is 1m and the cylinder is 5m long.

Homework Equations

The Attempt at a Solution

Not sure where to start really, or where to go.

Started with:

partial circle = 1/2 * r2 * (3.14 * theta/180)-sin theta

Not sure where to go with this using integration to solve.


HELP, please

 

[LCKurtz]

You haven't told us the orientation the tank has on the bottom of the lake. If it is upright the problem is very easy. If it is at an angle from upright the problem becomes difficult. With luck, if the tank is lying on its side, the problem becomes a routine calculus problem. In that case the end of the tank can be thought of as a circle in the xy plane and the volume of the contents is just the height of the cylinder times the covered area of the end.

So you just to integrate from the bottom of the circle up to an unknown depth d so that the resulting area is 1/4, 1/2, etc. the full area of the circle.

Do you see how to set up the integral?