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 with equal bases and the same height are in the ratio 1:2:3, we will calculate the volumes of each shape step by step.

### Step 1: Define Variables
Let the radius of the base of the cone, hemisphere, and cylinder be \( r \) and the height of each shape be \( h \).

### Step 2: Volume of the Cone
The formula for the volume \( V \) of a cone is given by:
\[
...