It takes approximately 20 square inches of felt to cover a tennis ball.
Explanation
A tennis ball is in shape of a Sphere. As the outside of the ball is covered with felt, so we need to find the surface area of the ball.
Formula for surface area of sphere: 
where,
is the radius of the sphere.
Here the radius is given as 1.25 inch, so 
Thus,

So, it takes approximately 20 square inches of felt to cover a tennis ball.