The radius of the penumbra is 17.5 cm, the radius of the total shadow is 7.5 cm. The umbra vanishes if the ball is at a height of 2.5 m. The dimensions of the umbra are constant if the radius of the ball is equal to the radius of the sphere.
The radius of the penumbra can be found from the similar triangles CC2D, BB1D, and AA2D (see the schematic diagram in Fig.). The radius of the umbra is obtained by considering triangles OA1A, OBBl, and OCC1 Line C2C1 is equal to the diameter of the sphere; line BB1 is equal to the radius of the ball; segments AC and AB are equal to the respective heights of the sphere and ball over the field.