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The question does not specify of what object the curved surface area is required. Without this information then a meaningful answer cannot be provided.
Assuming you mean a rectangular prism, you get the smallest surface area if the prism is a cube. You can calculate the required length of side to get that volume; then, based on that, the corresponding surface area.
Area is a plane or surface measurement. Depth is not required. Multiply the length by the width.
The answer depends on the shape whose surface area for which a formula is required.
It is the surface area of the two ends plus the surface area of the curved surface. Surface area of each end is pir2 Surface area of the curved surface is 2pirh Total surface area = 2pir2 + 2pirh