Buoyant force is directly proportional to the volume of the submerged solid. This means that the greater the volume of the solid that is submerged in the water, the greater the buoyant force will be. This is because the buoyant force is equal to the weight of the water that is displaced by the solid. So, if more of the solid is submerged, more water will be displaced, and therefore, the buoyant force will be greater.

Mathematically, the relationship between buoyant force and the volume of the submerged solid can be expressed using the following formula:

$$F_b = \rho *g* V$$

- F_b represents the buoyant force exerted by the water on the object in Newtons (N).

- ρ is the density of the fluid in kg/m³. In the case of water, the density is approximately 1000 kg/m³.

- g is the acceleration due to gravity on Earth, approximately 9.8 m/s².

- V is the volume of the submerged object or the volume of water displaced by the object in cubic meters (m³).

From this formula, it is evident that the buoyant force is directly proportional to the volume of the submerged solid. If the volume increases, the buoyant force also increases.