The cooling towers usually have the shape of a hyperboloid (as shown in the picture below). More specifically, it is a hyperboloid with inward-curved shape instead of outward-curved shape, which we can call the negative Gaussian curvature. This design is widely used in the cooling tower construction because by experiments the hyperboloid structure can better support and stabilize an object high off the ground compared to “straight” structure when all else equal, and the negative Gaussian curvature allows the whole structure to be economically efficient to build, since it only requires straight beams (as shown in the picture below).
The other reason for why hyperboloid shape is chosen, has something to do with its physical advantages. To explain, the wide bottom allows more interaction of heat and water to occur, the narrow waist accelerates the laminar flow of evaporated water, and the slightly wider top helps heated air to mix into the atmosphere. These factors all together elevates the efficiency cooling, which is the main purpose the tower.