# Volume of apple juice

1. Mar 30, 2014

### alingy2

A cylindrical container of height 1 m and diameter 0.5 m is partially filled with apple juice. When the container is lying on its side, the juice level at the deepest point is 37.5 cm (three eighths of a meter from the bottom of the cylinder is full). What is the liquid level after the container is raised up?

What I thought of doing is that I found the intersection of the radius with the point where the juice is at its maximum. By using Pythagoras and trig functions, I could find the angle from which the radius goes from the center to the top of the juice.

Now, I use the shell method, but instead of using 2pi, I used 4.1888.

Integral of 4.188*y*(0.25) dy
Then I added the triangular pyramid that was chopped off.

Is my method correct? Could you please tell me how you would do this.

2. Mar 30, 2014

### Simon Bridge

What triangular pyramid? Sounds confused.
Why not use the slice method ... sketch the cylinder end-on and divide the filled section into horizontal slices.