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Leaves are broad, thin and flat to provide a large surface area, to absorb sunlight for photosynthesis. :)
large area
The question does not specify of what object the curved surface area is required. Without this information then a meaningful answer cannot be provided.
The Alveoli
If the surface area of the organism is small, then there is no problem with getting all the oxygen needed. If the surface area of the organism is large, therefore a special respiratory surface is needed. An example is lungs, gills. The ratio of surface area to volume in a small organism is greater than the ratio in a large organism.