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Yes curved surface area and lateral surface area have the same meaning. Just because the lateral surface area of a cylinder is curved, the LSA of a cylinder is also known as its curved surface area.

Cyllinder's CSA = 2π r h

Cube's LSA = 4 a ²

Cuboid's LSA = 2( hl+bh). 

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Curved Surface Area is also called as Lateral Surface Area.......

CSA or LSA of Cylinder ( Solid) = 2π r h
CSA or LSA of  Cylinder ( Hollow) = Inner = 2π r h
                                                  = Outer = 2π R H

CSA or LSA of Cube = 4 a²

CSA or LSA of Cuboid= 2 ( l + b ) ×h    
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