Surface area

The surface area of a solid is the total exposed area that it has. For example, the surface area of a cube is the sum of the areas of its six square faces; the surface area of a tetrahedron is the sum of the area of its four triangular faces. In general, for any polyhedron without holes, the surface area is just the sum of the areas of the faces of the polyhedron. Some other solids, such as the cylinder and right cone, have surface areas that can be computed relatively easily. However, for most solids, calculus is necessary to compute the surface area.

For cubes, the surface area is $6s^2$

For a rectangular prism, the surface area is $2\cdot (lw+hw+lh)$, where l,w, and h are the length, width and height, respectively.

For spheres, the surface area is $4\pi \cdot r^2$.

For cylinders, the surface area is $2\pi \cdot rh+2\pi \cdot r^2$.

For cones, the surface area is $\pi \cdot r \cdot (r+\sqrt{h^2+r^2})$

For pyramids, the surface area is $lw+l \cdot \sqrt{(\frac{w}{2})^2+h^2}+w^2 \cdot \sqrt{(\frac{l}{2})^2+h^2}$.