How to find the height, given the volume of a cylinder and cone (conjoined together)? Here is a picture for a diagram: !enter image description here If water fills this "vase" up to half its capacity (NOT half its height), what will the height of the water be, starting from the bottom? And if you could explain the steps leading up the answer, that would be great. Thanks! EDIT: Sorry, the diagram didn't have the volume, here it is: Volume of cylinder: 1398cm cubed. Volume of Cone: 162.32cm cubed. Total volume: 1560.32cm cubed.

Assuming that "halfway point" means "half of the volume of the object is filled", here are the steps:

1. Find the volume of the object.

* Find the volume of the cone.
* Find the volume of the cylinder.
* Add those numbers together.


2. Divide the volume of the object by 2 to obtain the volume of water that will be added.

3. Add the water to the object and see how high it goes.

* The volume of the water will be greater than the volume of the conical part of the object, so subtract the volume of the cone from the volume of the water to obtain the volume of water that reaches the cylindrical part.

* The volume of the water reaching the cylindrical part will form a cylinder of the same radius as the cylindrical part, but with an unknown height. Solve for this height, knowing the volume and radius.

* Add the height of the cone.