A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio `1` : `2` : `3`.

Explanation

To show that the volumes of a cone, a hemisphere, and a cylinder standing on equal bases and having the same height are in the ratio 1 : 2 : 3, we will follow these steps:

### Step 1: Define the dimensions
Let the radius of the base of the cone, hemisphere, and cylinder be \( r \). Since they all have the same height, let the height of the cone and the cylinder be \( h \). For the hemisphere, the height is also equal to the radius \( r \).