9.21: Here is a diagram that might help:

This is the view obtained by cutting with a plane through the center of both spheres, and the center of the base of the cone. Since you know the radius of the bigger sphere, and the radius of the base of the cone, you can find the height of the cone. Then use similar triangles to find the radius of the smaller sphere.

9.23: The volume of any pyramid can be calculated by $V = \dfrac{A \times h}{3}$, where $A$ is the area of its base, and $h$ is its height.

9.25: Take a look at the view obtained by cutting with a vertical plane that goes through the diagonal of the square formed by the centers of the spheres of radius $1$.