4.1. A smooth sphere with a radius of 1 cm was dipped in red paint and launched between two perfectly smooth concentric spheres with radii of 4 cm and 6 cm, respectively (this sphere ended up outside the smaller sphere but inside the larger one). Upon touching both spheres, the sphere leaves a red trail. During its movement, the sphere traveled along a closed path, resulting in a red-contoured area on the smaller sphere with an area of 37 square cm. Find the area of the region bounded by the red contour on the larger sphere. Provide the answer in square centimeters, rounding to the nearest hundredth if necessary.