Mensuration - Surface Area of Cube, Cuboid, and Cylinder

Surface Area is the total region occupied by the outer surfaces of a three-dimensional object. Imagine 'unwrapping' a 3D shape into a flat 2D pattern called a 'net'; the total area of all the shapes in that net equals the surface area.

A Cuboid is a solid figure bounded by six rectangular faces. Visually, it resembles a rectangular box or a brick, defined by three dimensions: length ($l$), breadth ($b$), and height ($h$). Opposite faces of a cuboid are identical in area.

A Cube is a special case of a cuboid where all six faces are identical squares. If you look at a standard playing die, you are seeing a cube where the length, breadth, and height are all equal to the edge length ($a$).

A Cylinder consists of two congruent circular bases joined by a curved surface. Imagine a standard soda can or a tube of rolled paper. Its geometry is defined by the radius ($r$) of its circular base and its vertical height ($h$).

Lateral Surface Area (LSA) or Curved Surface Area (CSA) refers to the area of the side faces only, excluding the top and bottom bases. For example, the LSA of a room represents the area of the four walls, while the CSA of a cylinder is the area of the curved part if you were to remove the circular lids.

Total Surface Area (TSA) is the sum of the areas of all faces of the solid. For a cuboid or cube, it is the sum of 6 faces; for a cylinder, it is the sum of the curved surface area and the areas of the two circular bases.

Units of Measurement: Since surface area is a measure of a 2D region on a 3D object, it is always expressed in square units, such as $cm^2$, $m^2$, or $mm^2$. Always ensure all dimensions are in the same unit before calculation.

Visualizing Area of 4 Walls: In practical applications involving a room (cuboid), the area of the four walls is calculated as $2h(l + b)$. This is derived by taking the perimeter of the floor ($2(l+b)$) and multiplying it by the height ($h$).