Two cones have their heights in the ratio `1 : 3` and the radii of their bases in the ratio `3 : 1`. Show that their volumes are in the ratio `3 : 1`

Explanation

To show that the volumes of two cones are in the ratio 3:1 given that their heights are in the ratio 1:3 and the radii of their bases are in the ratio 3:1, we can follow these steps:

### Step 1: Define the Variables
Let:
- The height of the first cone be \( h_1 \)
- The height of the second cone be \( h_2 \)
- The radius of the base of the first cone be \( r_1 \)
- The radius of the base of the second cone be \( r_2 \)
...