Two vessels have the same area but different shapes. The first shapes takes twice the volume of water that the second vessel requires to fill up to a particular common height? Is the force exerted by the water on the base of the vessel the same in the two cases? If so, why do the vessels filled with water to that same height give different readings on a weighing scale?

Explanation

Pressure (and therefore force) on the two equal base areas are identical . But force is exerted by water on the sides of the vessels also. Which has a nonzero vertical component when the sides of the vessel are not perfectly normal to the base. Thus net vertical component of force by water on sides of the vessel is greater for the first vessel than the second. hence the vessels weigh different even when the force on the base is the same in the two cases.