The correct answer is: A. product of pressure intensity at its centroid and area.
The pressure intensity at a point is the force per unit area acting on a surface at that point. The centroid of a surface is the point where the entire weight of the surface can be considered to act. The area of a surface is the total amount of space enclosed by the surface.
The horizontal component of force on a curved surface is equal to the product of the pressure intensity at the centroid of the surface and the area of the surface. This is because the pressure intensity at the centroid is the average pressure acting on the surface, and the area of the surface is the total amount of space that the force is acting on.
The other options are incorrect because they do not take into account the pressure intensity at the centroid of the surface. Option B is the force on a vertical projection of the curved surface. This is not the same as the horizontal component of force on the curved surface, because the vertical projection of the curved surface is not necessarily horizontal. Option C is the weight of liquid vertically above the curved surface. This is not the same as the horizontal component of force on the curved surface, because the weight of liquid vertically above the curved surface is not necessarily acting horizontally. Option D is the force on the horizontal projection of the curved surface. This is not the same as the horizontal component of force on the curved surface, because the horizontal projection of the curved surface is not necessarily the same as the entire curved surface.