Surface Area: Definition and Types

Surface Area is the total area that covers the outer surface of a 3D object. It is classified into two main types based on the structure of the object:

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Types of Surface Area

1. Curved Surface Area (CSA):

• Refers to the area of only the curved surface of an object.
• Applicable to shapes like cylinders, cones, hemispheres, and spheres.
• Excludes any flat surfaces (like the bases of a cylinder or cone).

2. Total Surface Area (TSA):

• Refers to the total area of all the surfaces (both curved and flat) of an object.
• It is the sum of the curved surface area and the area of the flat surfaces (if any).

3. Lateral Surface Area (LSA):

• Refers to the area of all the vertical sides of an object, excluding the top and bottom faces.
• Typically used for prisms, cubes, and cuboids.

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Surface Area Formulas for Different Shapes

1. Sphere

• Description: A perfectly round 3D shape where all points on the surface are equidistant from the center.
• Curved Surface Area (CSA):

   • As the sphere has no flat surfaces, CSA and TSA are the same.
• Total Surface Area (TSA):

2. Cylinder

• Description: A 3D shape with two parallel circular bases connected by a curved surface.
• Curved Surface Area (CSA):

   • Includes only the curved lateral surface.
• Total Surface Area (TSA):


   • Includes the CSA and the areas of the two circular bases.

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3. Hemisphere

• Description: Half of a sphere with a flat circular base.
• Curved Surface Area (CSA):

   • Covers only the curved portion.
• Total Surface Area (TSA):


   • Includes the CSA and the flat circular base.

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4. Cone

• Description: A solid with a circular base and a curved surface tapering to a single point (vertex).
• Curved Surface Area (CSA):

   • Includes only the slant surface.
• Total Surface Area (TSA):


   • Includes the CSA and the circular base area.
   • l = √(r² + h²): Slant height.

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5. Cube

• Description: A solid with six equal square faces.
• Lateral Surface Area (LSA):

   • Includes only the four vertical faces.
• Total Surface Area (TSA):


   • Includes all six faces.

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6. Cuboid

• Description: A solid with six rectangular faces, where opposite faces are equal.
• Lateral Surface Area (LSA):

   • Includes the four vertical faces, excluding the top and bottom.
• Total Surface Area (TSA):


   • Includes all six rectangular faces.

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Summary Table of Surface Areas

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Key Notes

• Curved Surface Area is relevant only for shapes with curved surfaces.
• Total Surface Area includes all the surfaces of a shape, curved and flat.
• For cube and cuboid, only TSA and LSAare applicable since they have no curved surfaces.