# Integration to Solve, points on a cylinder

• katmarie
In summary, the problem at hand is determining the points on a measuring rod inside a cylindrical tank buried beneath a lake that would indicate when the tank is 1/4, 1/2, and 3/4 full. The tank has a diameter of 1m and is 5m long. The approach to solving this problem involves using integration to find the unknown depth d of the tank at which the covered area of the end is equal to 1/4, 1/2, and 3/4 of the full area of the circle. This can be done by setting up an integral from the bottom of the circle up to d and solving for d. The orientation of the tank on the bottom of the lake

## 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.

## 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.