Introduction:
When two metallic spheres are connected together and charged, the charge distribution between them depends on their capacitance. The capacitance is directly proportional to the radius of the spheres. Hence, the charge shared between the spheres will be in the ratio of their radii.

Explanation:
To understand why the charge shared between two metallic spheres is in the ratio of their radii, let's consider the following points:

1. Capacitance:
The capacitance of a conductor depends on its size and shape. For a spherical conductor, the capacitance is given by the formula C = 4πε₀r, where C is the capacitance, ε₀ is the vacuum permittivity, and r is the radius of the sphere. Therefore, we can see that the capacitance is directly proportional to the radius of the sphere.

2. Charge distribution:
When two metallic spheres are connected together, they form a parallel plate capacitor. The charge on each sphere will distribute in such a way that the potential difference between them is equal. This means that the charge on each sphere is directly proportional to its capacitance.

3. Law of Capacitance:
According to the law of capacitance, the charge on a capacitor is directly proportional to its capacitance. Mathematically, we can express this as Q ∝ C, where Q is the charge and C is the capacitance.

4. Charge ratio based on capacitance:
Since the charge on each sphere is directly proportional to its capacitance, and the capacitance is directly proportional to the radius of the sphere, we can conclude that the charge ratio between the spheres is the same as the ratio of their radii.

Conclusion:
In conclusion, the charge shared between two metallic spheres connected together will be in the ratio of their radii. This is because the charge distribution depends on the capacitance of the spheres, which is directly proportional to their radii.