Final answer:
The formula for lateral surface area varies depending on the shape, but it typically involves the perimeter of the base times the height for prisms and cylinders, and πrℯ for cones.
Step-by-step explanation:
Lateral Surface Area Formulas
The formula for lateral surface area depends on the type of geometric solid we are dealing with. However, each formula generally involves multiplying the perimeter (or circumference) of the base shape by the height of the solid. For example, the lateral surface area of a cylinder can be calculated by multiplying the circumference of the circle (which is 2πr) by the height (h), giving us the formula Lateral Surface Area = 2πrh. Remember that this does not include the areas of the top and bottom faces of the cylinder.
Cylinders aren't the only shapes with lateral surface area. For a prism, the lateral surface area is the perimeter of the base times the height of the prism. Similarly, for a cone, you'd use the formula Lateral Surface Area = πrℯ, where l is the slant height of the cone.
It's important to understand that the concept of lateral surface area is pertinent when you want the area of the sides of a solid without including its bases or caps. This can be useful in real-world applications where, for example, material cost for building a storage tank is based on the material needed for the side walls.