You cannot assume that the bowl is hemispherical. The bowl is a portion of a sphere but not half of it. In this case the centre of the theoretical sphere which makes the bowl is O which is above the bowl. The radius of this imaginary sphere is a, which is side OB. The r is NOT the radius of this sphere, but is the radius of the CIRCULAR MOTION of the particle (not the sphere making up the bowl).
The reason the normal force of the particle is at an angle is because if you imagine a complete sphere, the normal force is perpendicular to the point on the sphere.