Lateral surface area or curved surface area is the area of all the sides of an object excluding the base and top. Total surface area is lateral surface area + area of base and top....

Lateral Surface Area:
The lateral surface area is the total surface area of a three-dimensional object minus the area of its base(s). It represents the sum of the areas of all the faces that are not bases. This measurement is particularly useful when calculating the amount of material needed to cover the sides of an object or when determining the surface area of a solid that does not have a top or bottom.

Curved Surface Area:
The curved surface area refers to the total surface area of a three-dimensional object that includes all the curved surfaces. It takes into account the areas of all the curved faces and excludes the areas of the base(s). This measurement is commonly used when calculating the surface area of objects with curved or rounded surfaces, such as cylinders, cones, and spheres.

Differences:
1. Definition: The lateral surface area is the total surface area minus the area of the bases, while the curved surface area includes only the curved surfaces of a three-dimensional object.
2. Components: The lateral surface area considers the sum of all the non-base faces, whereas the curved surface area includes only the curved faces of an object.
3. Objects: The lateral surface area can be applied to a variety of objects, including prisms, pyramids, and polyhedra, whereas the curved surface area is primarily used for objects with curved or rounded surfaces, such as cylinders, cones, and spheres.
4. Calculation: To calculate the lateral surface area, one needs to find the sum of the areas of all the non-base faces. In contrast, to determine the curved surface area, the areas of all the curved faces are added together.
5. Applications: The lateral surface area is often used to estimate the amount of material needed to cover the sides of an object or to determine the surface area of a solid without top or bottom faces. On the other hand, the curved surface area is useful in various fields like architecture, engineering, and design, where objects with curved surfaces are common.

In summary, the lateral surface area differs from the curved surface area in terms of the components considered, the types of objects it is applicable to, the calculation method, and the practical applications. Understanding these differences is essential for accurately measuring and calculating the surface area of various three-dimensional objects.