No, the rigid structure of the sphere does not prevent the water from exerting its pressure on the air inside the sphere. In fact, the pressure exerted by a fluid such as water is transmitted uniformly in all directions, including inwards towards the interior of an enclosed space like the sphere.
When the sphere is submerged in water, the water exerts pressure on all surfaces of the sphere, including its outer surface. This pressure is transmitted through the walls of the sphere and affects the air inside. The rigid structure of the sphere helps maintain its shape and prevents it from collapsing under the pressure exerted by the water.
The pressure inside the sphere will be the result of a balance between the pressure exerted by the water on the outside and the pressure exerted by the air on the inside. The pressure inside the sphere will increase with increasing depth because the weight of the water above adds to the pressure.
In summary, the rigid structure of the sphere does not prevent the water from exerting pressure on the air inside. The pressure exerted by the water is transmitted through the walls of the sphere and affects the air inside, resulting in a balanced pressure distribution within the sphere.