### Find the volume of the biggest cone that can fit inside a cube of side 3 cm.

 9π 4
cm3

Step by Step Explanation:
1. The volume of a cone is of radius r and height h =
 1 3
πr2h.
2. Since we have to fit it inside a cube of side 3 cm, we see that the diameter of the cone will be 3 cm, and the height will be 3 cm (A cone larger than this in diameter or height will not fit inside the cube).
3. So, the radius of this cone =
 3 2
cm = 1.5 cm
4. Putting these values into the equation of the volume, we get the volume of the cone =
 1 3
× π × (
 3 2
)2 × 3 cm3
5. On solving, we get the volume of the cone =
 9π 4
cm3