Finding remaining volume of water in a cylinder.

[Oalvarez]

I have a problem for a written assignment in my calc 2 class involving the volume of a cylindrical glass.

A cylindrical drinking glass 10 in tall and 4 in in diameter is filled with water, and then tilted so that the water pours out until half the base is exposed. Write an integral to find the volume of the water remaining in the glass.I know that the initial volume is going to be 40pi in³, but I really don't know where to go from there. I have a feeling that it might have something to do with related rates. However, the fact that I have to set up an integral makes me doubt that initial hunch. Thanks in advanced for any help.

 

[RUber]

If you draw the picture in 2D you should see a right triangle with height 10 and base 2. Changing to 3D, you will have a semi-circle at the base.
Consider integrating the area of the partial-circle over 0 to 10.

 

[LCKurtz]

I have a problem for a written assignment in my calc 2 class involving the volume of a cylindrical glass.

A cylindrical drinking glass 10 in tall and 4 in in diameter is filled with water, and then tilted so that the water pours out until half the base is exposed. Write an integral to find the volume of the water remaining in the glass.I know that the initial volume is going to be 40pi in³, but I really don't know where to go from there. I have a feeling that it might have something to do with related rates. However, the fact that I have to set up an integral makes me doubt that initial hunch. Thanks in advanced for any help.

You are correct that it has nothing to do with related rates. I would draw a picture with the cylinder sitting above the origin in the xy plane. The surface of the water is then a slanted plane and you want the volume under the plane above the semicircle.