Lateral and total surface area of prisms, pyramids, cylinders, cones, and spheres

Surface area measures the total area of a solid's outer surface. Lateral area counts only the sides, while total surface area also includes the bases. For a prism, lateral area = perimeter of the base x height, and total = lateral area + 2 x base area. For a cylinder, lateral area = 2 x pi x r x h and total = 2 x pi x r x h + 2 x pi x r^2, so a cylinder with radius 3 and height 5 has a lateral area of 30 pi (about 94.2) and a total surface area of 48 pi (about 150.8) square units. For a regular pyramid, lateral area = (1/2) x perimeter of the base x slant height, plus the base for the total; for a cone, lateral area = pi x r x l, where l is the slant height, plus pi x r^2 for the total. A sphere has surface area 4 x pi x r^2, so a sphere of radius 3 has 36 pi. For a composite solid, add only the faces that are actually on the outside.

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